Subgroups — C₉×#2424 #11767145

Order 1152.

1383 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#120	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#396	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#394	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#392	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#388	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2424	C₃	1	1	yes	maximal, characteristic
17	C₂⁵×C₉	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
22	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
23	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
24	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
26	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
27	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
28	C₉×#121	—	2	4	no	—
29	C₉×#121	—	2	4	no	—
30	C₉×#120	—	2	4	no	—
31	C₉×#120	—	2	4	no	—
32	C₄×D₄×C₉	—	2	4	no	—
33	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₉×C₂²⋊C₄	—	2	4	no	—
38	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
54	C₉×#95	C₂²	1	1	yes	characteristic, complemented
55	C₉×#95	C₂²	1	1	yes	characteristic, complemented
56	C₉×#95	C₂²	1	1	yes	characteristic, complemented
57	C₉×#95	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
59	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
60	C₂×C₃×#120	C₂×C₃	1	1	yes	characteristic
61	C₂×C₃×#120	C₂×C₃	1	1	yes	characteristic
62	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
63	C₂²×C₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
64	C₃×#396	C₂×C₃	1	1	yes	characteristic
65	C₃×#394	C₂×C₃	1	1	yes	characteristic
66	C₃×#394	C₂×C₃	1	1	yes	characteristic
67	C₃×#392	C₂×C₃	1	1	yes	characteristic
68	C₃×#390	C₂×C₃	1	1	yes	characteristic
69	C₃×#388	C₂×C₃	1	1	yes	characteristic
70	C₃×#386	C₂×C₃	1	1	yes	characteristic
71	C₃×#386	C₂×C₃	1	1	yes	characteristic
72	C₃×#385	C₂×C₃	1	1	yes	characteristic
73	C₂⁴×C₉	—	2	2	no	—
74	C₂⁴×C₉	—	2	2	no	—
75	C₂⁴×C₉	—	2	2	no	—
76	C₂⁴×C₉	—	2	2	no	—
77	C₂⁴×C₉	—	2	2	no	—
78	C₂⁴×C₉	—	4	1	no	—
79	C₂⁴×C₉	—	4	1	no	—
80	C₂⁴×C₉	C₂³	1	1	yes	characteristic
81	C₂⁴×C₉	C₂³	1	1	yes	characteristic
82	C₂⁴×C₉	C₂³	1	1	yes	characteristic
83	C₂⁴×C₉	C₂³	1	1	yes	characteristic
84	C₂⁴×C₉	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₉	—	2	2	no	—
86	C₂×D₄×C₉	—	2	2	no	—
87	C₂×D₄×C₉	—	2	2	no	—
88	C₂×D₄×C₉	—	2	2	no	—
89	C₂×D₄×C₉	—	2	2	no	—
90	C₂×D₄×C₉	—	2	2	no	—
91	C₂×D₄×C₉	—	2	2	no	—
92	C₂×D₄×C₉	—	2	2	no	—
93	C₂×D₄×C₉	—	2	2	no	—
94	C₂×D₄×C₉	—	2	2	no	—
95	C₂×D₄×C₉	—	2	2	no	—
96	C₂×D₄×C₉	—	2	2	no	—
97	C₂×D₄×C₉	—	2	2	no	—
98	C₂×D₄×C₉	—	2	2	no	—
99	C₂×D₄×C₉	—	2	2	no	—
100	C₂×D₄×C₉	—	4	1	no	—
101	C₂×D₄×C₉	—	4	1	no	—
102	C₂×D₄×C₉	—	4	1	no	—
103	C₂×D₄×C₉	—	4	1	no	—
104	C₂×D₄×C₉	—	4	1	no	—
105	C₂×D₄×C₉	D₄	1	4	yes	complemented
106	C₂²×C₄×C₉	—	2	2	no	—
107	C₂²×C₄×C₉	—	2	2	no	—
108	C₂²×C₄×C₉	—	2	2	no	—
109	C₂²×C₄×C₉	—	2	2	no	—
110	C₂²×C₄×C₉	—	2	2	no	—
111	C₂²×C₄×C₉	—	2	2	no	—
112	C₂²×C₄×C₉	—	4	1	no	—
113	C₂²×C₄×C₉	—	4	1	no	—
114	C₂²×C₄×C₉	—	4	1	no	—
115	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
124	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
125	C₉×C₄⋊C₄	—	2	2	no	—
126	C₉×C₄⋊C₄	—	2	2	no	—
127	C₉×C₄⋊C₄	—	2	2	no	—
128	C₉×C₄⋊C₄	—	4	1	no	—
129	C₉×C₂²⋊C₄	—	2	2	no	—
130	C₉×C₂²⋊C₄	—	2	2	no	—
131	C₉×C₂²⋊C₄	—	2	2	no	—
132	C₉×C₂²⋊C₄	—	2	2	no	—
133	C₉×C₂²⋊C₄	—	2	2	no	—
134	C₉×C₂²⋊C₄	—	2	2	no	—
135	C₉×C₂²⋊C₄	—	2	2	no	—
136	C₉×C₂²⋊C₄	—	2	2	no	—
137	C₉×C₂²⋊C₄	—	2	2	no	—
138	C₉×C₂²⋊C₄	—	2	2	no	—
139	C₉×C₂²⋊C₄	—	2	2	no	—
140	C₉×C₂²⋊C₄	—	2	2	no	—
141	C₉×C₂²⋊C₄	—	4	1	no	—
142	C₉×C₂²⋊C₄	D₄	1	4	yes	complemented
143	C₉×C₂²⋊C₄	D₄	1	4	yes	complemented
144	C₄²×C₉	—	2	2	no	—
145	#2424	C₉	1	1	yes	characteristic, direct product factor, Sylow
146	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
147	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
148	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
149	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
150	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
151	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
153	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
154	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
155	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
156	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
157	C₃×#121	—	2	4	no	—
158	C₃×#121	—	2	4	no	—
159	C₃×#120	—	2	4	no	—
160	C₃×#120	—	2	4	no	—
161	C₃×C₄×D₄	—	2	4	no	—
162	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
167	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
181	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
182	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
183	C₃×#95	C₂²×C₃	1	1	yes	characteristic
184	C₃×#95	C₂²×C₃	1	1	yes	characteristic
185	C₃×#95	C₂²×C₃	1	1	yes	characteristic
186	C₃×#95	C₂²×C₃	1	1	yes	characteristic
187	C₂³×C₉	—	2	1	no	—
188	C₂³×C₉	—	2	1	no	—
189	C₂³×C₉	—	2	1	no	—
190	C₂³×C₉	—	2	1	no	—
191	C₂³×C₉	—	2	8	no	—
192	C₂³×C₉	—	2	1	no	—
193	C₂³×C₉	—	2	1	no	—
194	C₂³×C₉	—	2	1	no	—
195	C₂³×C₉	—	2	1	no	—
196	C₂³×C₉	—	2	1	no	—
197	C₂³×C₉	—	2	1	no	—
198	C₂³×C₉	—	2	1	no	—
199	C₂³×C₉	—	2	1	no	—
200	C₂³×C₉	—	2	1	no	—
201	C₂³×C₉	—	2	1	no	—
202	C₂³×C₉	—	2	1	no	—
203	C₂³×C₉	—	2	1	no	—
204	C₂³×C₉	—	2	1	no	—
205	C₂³×C₉	—	2	1	no	—
206	C₂³×C₉	—	2	1	no	—
207	C₂³×C₉	—	2	1	no	—
208	C₂³×C₉	—	2	1	no	—
209	C₂³×C₉	—	2	1	no	—
210	C₂³×C₉	—	2	1	no	—
211	C₂³×C₉	—	2	1	no	—
212	C₂³×C₉	—	2	1	no	—
213	C₂³×C₉	—	2	1	no	—
214	C₂³×C₉	—	2	1	no	—
215	C₂³×C₉	—	2	1	no	—
216	C₂³×C₉	—	2	1	no	—
217	C₂³×C₉	—	4	4	no	—
218	C₂³×C₉	—	4	4	no	—
219	C₂³×C₉	—	4	4	no	—
220	C₂³×C₉	—	4	4	no	—
221	C₂³×C₉	—	4	4	no	—
222	C₂³×C₉	—	4	4	no	—
223	C₂³×C₉	C₂×D₄	1	2	yes	—
224	C₂³×C₉	C₂×D₄	1	2	yes	—
225	C₂³×C₉	C₂×D₄	1	2	yes	—
226	C₂³×C₉	C₂×D₄	1	2	yes	—
227	C₂³×C₉	#41	1	2	yes	—
228	C₂³×C₉	#41	1	2	yes	—
229	C₂³×C₉	C₂⁴	1	1	yes	characteristic
230	D₄×C₉	—	2	8	no	—
231	D₄×C₉	—	4	4	no	—
232	D₄×C₉	—	4	4	no	—
233	D₄×C₉	—	4	4	no	—
234	D₄×C₉	—	4	4	no	—
235	D₄×C₉	—	4	4	no	—
236	D₄×C₉	—	4	4	no	—
237	C₂×C₄×C₉	—	2	1	no	—
238	C₂×C₄×C₉	—	2	1	no	—
239	C₂×C₄×C₉	—	2	1	no	—
240	C₂×C₄×C₉	—	2	1	no	—
241	C₂×C₄×C₉	—	2	1	no	—
242	C₂×C₄×C₉	—	2	1	no	—
243	C₂×C₄×C₉	—	2	1	no	—
244	C₂×C₄×C₉	—	2	1	no	—
245	C₂×C₄×C₉	—	2	1	no	—
246	C₂×C₄×C₉	—	2	1	no	—
247	C₂×C₄×C₉	—	2	1	no	—
248	C₂×C₄×C₉	—	2	1	no	—
249	C₂×C₄×C₉	—	2	1	no	—
250	C₂×C₄×C₉	—	2	1	no	—
251	C₂×C₄×C₉	—	2	1	no	—
252	C₂×C₄×C₉	—	2	1	no	—
253	C₂×C₄×C₉	—	2	1	no	—
254	C₂×C₄×C₉	—	2	1	no	—
255	C₂×C₄×C₉	—	2	1	no	—
256	C₂×C₄×C₉	—	2	1	no	—
257	C₂×C₄×C₉	—	2	1	no	—
258	C₂×C₄×C₉	—	2	1	no	—
259	C₂×C₄×C₉	—	2	1	no	—
260	C₂×C₄×C₉	—	2	1	no	—
261	C₂×C₄×C₉	—	2	1	no	—
262	C₂×C₄×C₉	—	4	4	no	—
263	C₂×C₄×C₉	—	4	4	no	—
264	C₂×C₄×C₉	—	4	4	no	—
265	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
266	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
267	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
268	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
269	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
270	C₂×#121	C₂×C₉	1	1	yes	characteristic, complemented
271	C₂×#121	C₂×C₉	1	1	yes	characteristic, complemented
272	C₂×#120	C₂×C₉	1	1	yes	characteristic, complemented
273	C₂×#120	C₂×C₉	1	1	yes	characteristic, complemented
274	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
275	C₂²×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
276	#396	C₂×C₉	1	1	yes	characteristic, complemented
277	#394	C₂×C₉	1	1	yes	characteristic, complemented
278	#394	C₂×C₉	1	1	yes	characteristic, complemented
279	#392	C₂×C₉	1	1	yes	characteristic, complemented
280	#390	C₂×C₉	1	1	yes	characteristic, complemented
281	#388	C₂×C₉	1	1	yes	characteristic, complemented
282	#386	C₂×C₉	1	1	yes	characteristic, complemented
283	#386	C₂×C₉	1	1	yes	characteristic, complemented
284	#385	C₂×C₉	1	1	yes	characteristic, complemented
285	C₂⁴×C₃	—	2	2	no	—
286	C₂⁴×C₃	—	2	2	no	—
287	C₂⁴×C₃	—	2	2	no	—
288	C₂⁴×C₃	—	2	2	no	—
289	C₂⁴×C₃	—	2	2	no	—
290	C₂⁴×C₃	—	4	1	no	—
291	C₂⁴×C₃	—	4	1	no	—
292	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
293	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
294	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
295	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
296	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₃×D₄	—	2	2	no	—
298	C₂×C₃×D₄	—	2	2	no	—
299	C₂×C₃×D₄	—	2	2	no	—
300	C₂×C₃×D₄	—	2	2	no	—
301	C₂×C₃×D₄	—	2	2	no	—
302	C₂×C₃×D₄	—	2	2	no	—
303	C₂×C₃×D₄	—	2	2	no	—
304	C₂×C₃×D₄	—	2	2	no	—
305	C₂×C₃×D₄	—	2	2	no	—
306	C₂×C₃×D₄	—	2	2	no	—
307	C₂×C₃×D₄	—	2	2	no	—
308	C₂×C₃×D₄	—	2	2	no	—
309	C₂×C₃×D₄	—	2	2	no	—
310	C₂×C₃×D₄	—	2	2	no	—
311	C₂×C₃×D₄	—	2	2	no	—
312	C₂×C₃×D₄	—	4	1	no	—
313	C₂×C₃×D₄	—	4	1	no	—
314	C₂×C₃×D₄	—	4	1	no	—
315	C₂×C₃×D₄	—	4	1	no	—
316	C₂×C₃×D₄	—	4	1	no	—
317	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
318	C₂²×C₃×C₄	—	2	2	no	—
319	C₂²×C₃×C₄	—	2	2	no	—
320	C₂²×C₃×C₄	—	2	2	no	—
321	C₂²×C₃×C₄	—	2	2	no	—
322	C₂²×C₃×C₄	—	2	2	no	—
323	C₂²×C₃×C₄	—	2	2	no	—
324	C₂²×C₃×C₄	—	4	1	no	—
325	C₂²×C₃×C₄	—	4	1	no	—
326	C₂²×C₃×C₄	—	4	1	no	—
327	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
328	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
329	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
330	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
331	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
332	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
335	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
336	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
337	C₃×C₄⋊C₄	—	2	2	no	—
338	C₃×C₄⋊C₄	—	2	2	no	—
339	C₃×C₄⋊C₄	—	2	2	no	—
340	C₃×C₄⋊C₄	—	4	1	no	—
341	C₃×C₂²⋊C₄	—	2	2	no	—
342	C₃×C₂²⋊C₄	—	2	2	no	—
343	C₃×C₂²⋊C₄	—	2	2	no	—
344	C₃×C₂²⋊C₄	—	2	2	no	—
345	C₃×C₂²⋊C₄	—	2	2	no	—
346	C₃×C₂²⋊C₄	—	2	2	no	—
347	C₃×C₂²⋊C₄	—	2	2	no	—
348	C₃×C₂²⋊C₄	—	2	2	no	—
349	C₃×C₂²⋊C₄	—	2	2	no	—
350	C₃×C₂²⋊C₄	—	2	2	no	—
351	C₃×C₂²⋊C₄	—	2	2	no	—
352	C₃×C₂²⋊C₄	—	2	2	no	—
353	C₃×C₂²⋊C₄	—	4	1	no	—
354	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
355	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
356	C₃×C₄²	—	2	2	no	—
357	C₂²×C₉	—	2	2	no	—
358	C₂²×C₉	—	2	2	no	—
359	C₂²×C₉	—	2	2	no	—
360	C₂²×C₉	—	2	2	no	—
361	C₂²×C₉	—	2	2	no	—
362	C₂²×C₉	—	2	2	no	—
363	C₂²×C₉	—	2	2	no	—
364	C₂²×C₉	—	2	2	no	—
365	C₂²×C₉	—	2	2	no	—
366	C₂²×C₉	—	2	2	no	—
367	C₂²×C₉	—	2	2	no	—
368	C₂²×C₉	—	2	2	no	—
369	C₂²×C₉	—	2	2	no	—
370	C₂²×C₉	—	2	2	no	—
371	C₂²×C₉	—	2	2	no	—
372	C₂²×C₉	—	4	16	no	—
373	C₂²×C₉	—	4	1	no	—
374	C₂²×C₉	—	4	1	no	—
375	C₂²×C₉	—	4	1	no	—
376	C₂²×C₉	—	4	1	no	—
377	C₂²×C₉	—	4	1	no	—
378	C₂²×C₉	—	4	1	no	—
379	C₂²×C₉	—	4	1	no	—
380	C₂²×C₉	—	4	1	no	—
381	C₂²×C₉	—	4	1	no	—
382	C₂²×C₉	—	4	1	no	—
383	C₂²×C₉	—	4	1	no	—
384	C₂²×C₉	—	4	1	no	—
385	C₂²×C₉	—	4	1	no	—
386	C₂²×C₉	—	4	1	no	—
387	C₂²×C₉	—	4	1	no	—
388	C₂²×C₉	—	4	1	no	—
389	C₂²×C₉	—	4	1	no	—
390	C₂²×C₉	—	4	1	no	—
391	C₂²×C₉	—	4	1	no	—
392	C₂²×C₉	#121	1	4	yes	complemented
393	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
394	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
395	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
396	C₂²×C₉	C₂×#41	1	1	yes	characteristic
397	C₂²×C₉	C₂×#41	1	1	yes	characteristic
398	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
399	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
400	C₄×C₉	—	2	2	no	—
401	C₄×C₉	—	2	2	no	—
402	C₄×C₉	—	2	2	no	—
403	C₄×C₉	—	2	2	no	—
404	C₄×C₉	—	2	2	no	—
405	C₄×C₉	—	4	1	no	—
406	C₄×C₉	—	4	1	no	—
407	C₄×C₉	—	4	1	no	—
408	C₄×C₉	—	4	1	no	—
409	C₄×C₉	—	4	1	no	—
410	C₂⁵	C₂²×C₉	1	1	yes	characteristic
411	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
412	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
413	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
414	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
415	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
416	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
417	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
418	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
419	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
420	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
421	#121	—	2	4	no	—
422	#121	—	2	4	no	—
423	#120	—	2	4	no	—
424	#120	—	2	4	no	—
425	C₄×D₄	—	2	4	no	—
426	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
427	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
428	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
429	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
430	C₂×C₂²⋊C₄	—	2	4	no	—
431	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
434	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
435	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
442	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
443	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
444	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
445	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
446	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
447	#95	C₂²×C₉	1	1	yes	characteristic, complemented
448	#95	C₂²×C₉	1	1	yes	characteristic, complemented
449	#95	C₂²×C₉	1	1	yes	characteristic, complemented
450	#95	C₂²×C₉	1	1	yes	characteristic, complemented
451	C₂³×C₃	—	2	1	no	—
452	C₂³×C₃	—	2	1	no	—
453	C₂³×C₃	—	2	1	no	—
454	C₂³×C₃	—	2	1	no	—
455	C₂³×C₃	—	2	8	no	—
456	C₂³×C₃	—	2	1	no	—
457	C₂³×C₃	—	2	1	no	—
458	C₂³×C₃	—	2	1	no	—
459	C₂³×C₃	—	2	1	no	—
460	C₂³×C₃	—	2	1	no	—
461	C₂³×C₃	—	2	1	no	—
462	C₂³×C₃	—	2	1	no	—
463	C₂³×C₃	—	2	1	no	—
464	C₂³×C₃	—	2	1	no	—
465	C₂³×C₃	—	2	1	no	—
466	C₂³×C₃	—	2	1	no	—
467	C₂³×C₃	—	2	1	no	—
468	C₂³×C₃	—	2	1	no	—
469	C₂³×C₃	—	2	1	no	—
470	C₂³×C₃	—	2	1	no	—
471	C₂³×C₃	—	2	1	no	—
472	C₂³×C₃	—	2	1	no	—
473	C₂³×C₃	—	2	1	no	—
474	C₂³×C₃	—	2	1	no	—
475	C₂³×C₃	—	2	1	no	—
476	C₂³×C₃	—	2	1	no	—
477	C₂³×C₃	—	2	1	no	—
478	C₂³×C₃	—	2	1	no	—
479	C₂³×C₃	—	2	1	no	—
480	C₂³×C₃	—	2	1	no	—
481	C₂³×C₃	—	4	4	no	—
482	C₂³×C₃	—	4	4	no	—
483	C₂³×C₃	—	4	4	no	—
484	C₂³×C₃	—	4	4	no	—
485	C₂³×C₃	—	4	4	no	—
486	C₂³×C₃	—	4	4	no	—
487	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
488	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
489	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
490	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
491	C₂³×C₃	C₃×#41	1	2	yes	—
492	C₂³×C₃	C₃×#41	1	2	yes	—
493	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
494	C₃×D₄	—	2	8	no	—
495	C₃×D₄	—	4	4	no	—
496	C₃×D₄	—	4	4	no	—
497	C₃×D₄	—	4	4	no	—
498	C₃×D₄	—	4	4	no	—
499	C₃×D₄	—	4	4	no	—
500	C₃×D₄	—	4	4	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	2	1	no	—
517	C₂×C₃×C₄	—	2	1	no	—
518	C₂×C₃×C₄	—	2	1	no	—
519	C₂×C₃×C₄	—	2	1	no	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	4	4	no	—
527	C₂×C₃×C₄	—	4	4	no	—
528	C₂×C₃×C₄	—	4	4	no	—
529	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
530	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
531	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
532	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
533	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
534	C₂×C₉	—	2	4	no	—
535	C₂×C₉	—	4	2	no	—
536	C₂×C₉	—	4	2	no	—
537	C₂×C₉	—	4	2	no	—
538	C₂×C₉	—	8	1	no	—
539	C₂×C₉	C₂×#121	1	1	yes	characteristic
540	C₂×C₉	#525	1	1	yes	characteristic
541	C₂×C₉	#538	1	1	yes	characteristic
542	C₂×C₉	D₄²	1	1	yes	characteristic
543	C₂×C₉	D₄²	1	1	yes	characteristic
544	C₂×C₉	#546	1	1	yes	characteristic
545	C₂×C₉	#546	1	1	yes	characteristic
546	C₂⁴	—	2	2	no	—
547	C₂⁴	—	2	2	no	—
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	4	1	no	—
552	C₂⁴	—	4	1	no	—
553	C₂⁴	C₂³×C₉	1	1	yes	characteristic
554	C₂⁴	C₂³×C₉	1	1	yes	characteristic
555	C₂⁴	C₂³×C₉	1	1	yes	characteristic
556	C₂⁴	C₂³×C₉	1	1	yes	characteristic
557	C₂⁴	C₂³×C₉	1	1	yes	characteristic
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	4	1	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	—	4	1	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂×D₄	D₄×C₉	1	4	yes	complemented
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	4	1	no	—
586	C₂²×C₄	—	4	1	no	—
587	C₂²×C₄	—	4	1	no	—
588	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
589	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
590	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
591	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
592	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
593	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
594	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
595	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
596	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
597	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	4	1	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	4	1	no	—
615	C₂²⋊C₄	D₄×C₉	1	4	yes	complemented
616	C₂²⋊C₄	D₄×C₉	1	4	yes	complemented
617	C₄²	—	2	2	no	—
618	C₂²×C₃	—	2	2	no	—
619	C₂²×C₃	—	2	2	no	—
620	C₂²×C₃	—	2	2	no	—
621	C₂²×C₃	—	2	2	no	—
622	C₂²×C₃	—	2	2	no	—
623	C₂²×C₃	—	2	2	no	—
624	C₂²×C₃	—	2	2	no	—
625	C₂²×C₃	—	2	2	no	—
626	C₂²×C₃	—	2	2	no	—
627	C₂²×C₃	—	2	2	no	—
628	C₂²×C₃	—	2	2	no	—
629	C₂²×C₃	—	2	2	no	—
630	C₂²×C₃	—	2	2	no	—
631	C₂²×C₃	—	2	2	no	—
632	C₂²×C₃	—	2	2	no	—
633	C₂²×C₃	—	4	16	no	—
634	C₂²×C₃	—	4	1	no	—
635	C₂²×C₃	—	4	1	no	—
636	C₂²×C₃	—	4	1	no	—
637	C₂²×C₃	—	4	1	no	—
638	C₂²×C₃	—	4	1	no	—
639	C₂²×C₃	—	4	1	no	—
640	C₂²×C₃	—	4	1	no	—
641	C₂²×C₃	—	4	1	no	—
642	C₂²×C₃	—	4	1	no	—
643	C₂²×C₃	—	4	1	no	—
644	C₂²×C₃	—	4	1	no	—
645	C₂²×C₃	—	4	1	no	—
646	C₂²×C₃	—	4	1	no	—
647	C₂²×C₃	—	4	1	no	—
648	C₂²×C₃	—	4	1	no	—
649	C₂²×C₃	—	4	1	no	—
650	C₂²×C₃	—	4	1	no	—
651	C₂²×C₃	—	4	1	no	—
652	C₂²×C₃	—	4	1	no	—
653	C₂²×C₃	C₃×#121	1	4	yes	—
654	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
655	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
656	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
657	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
658	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
659	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
660	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
661	C₃×C₄	—	2	2	no	—
662	C₃×C₄	—	2	2	no	—
663	C₃×C₄	—	2	2	no	—
664	C₃×C₄	—	2	2	no	—
665	C₃×C₄	—	2	2	no	—
666	C₃×C₄	—	4	1	no	—
667	C₃×C₄	—	4	1	no	—
668	C₃×C₄	—	4	1	no	—
669	C₃×C₄	—	4	1	no	—
670	C₃×C₄	—	4	1	no	—
671	C₉	#2424	1	1	yes	characteristic, direct product factor, Sylow
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	8	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	4	4	no	—
703	C₂³	—	4	4	no	—
704	C₂³	—	4	4	no	—
705	C₂³	—	4	4	no	—
706	C₂³	—	4	4	no	—
707	C₂³	—	4	4	no	—
708	C₂³	C₂×D₄×C₉	1	2	yes	—
709	C₂³	C₂×D₄×C₉	1	2	yes	—
710	C₂³	C₂×D₄×C₉	1	2	yes	—
711	C₂³	C₂×D₄×C₉	1	2	yes	—
712	C₂³	C₉×#41	1	2	yes	—
713	C₂³	C₉×#41	1	2	yes	—
714	C₂³	C₂⁴×C₉	1	1	yes	characteristic
715	D₄	—	2	8	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	4	no	—
720	D₄	—	4	4	no	—
721	D₄	—	4	4	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	4	no	—
749	C₂×C₄	—	4	4	no	—
750	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
751	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
752	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
753	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
754	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
755	C₂×C₃	—	2	4	no	—
756	C₂×C₃	—	4	2	no	—
757	C₂×C₃	—	4	2	no	—
758	C₂×C₃	—	4	2	no	—
759	C₂×C₃	—	8	1	no	—
760	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
761	C₂×C₃	C₃×#525	1	1	yes	characteristic
762	C₂×C₃	C₃×#538	1	1	yes	characteristic
763	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
764	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
765	C₂×C₃	C₃×#546	1	1	yes	characteristic
766	C₂×C₃	C₃×#546	1	1	yes	characteristic
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	4	16	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	C₉×#121	1	4	yes	complemented
803	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
804	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
805	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
806	C₂²	C₂×C₉×#41	1	1	yes	characteristic
807	C₂²	C₂×C₉×#41	1	1	yes	characteristic
808	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
809	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
810	C₄	—	2	2	no	—
811	C₄	—	2	2	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₃	C₃×#2424	1	1	yes	characteristic
821	C₂	—	2	4	no	—
822	C₂	—	4	2	no	—
823	C₂	—	4	2	no	—
824	C₂	—	4	2	no	—
825	C₂	—	8	1	no	—
826	C₂	C₂×C₉×#121	1	1	yes	characteristic
827	C₂	C₉×#525	1	1	yes	characteristic
828	C₂	C₉×#538	1	1	yes	characteristic
829	C₂	D₄²×C₉	1	1	yes	characteristic
830	C₂	D₄²×C₉	1	1	yes	characteristic
831	C₂	C₉×#546	1	1	yes	characteristic
832	C₂	C₉×#546	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₃×#2424	C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#121	C₂	semidirect
2. C₂×C₉×#121	C₂	semidirect
3. C₂×C₉×#120	C₂	semidirect
4. C₂×C₉×#120	C₂	semidirect
5. C₂×C₄×D₄×C₉	C₂	semidirect
6. C₂²×C₉×C₂²⋊C₄	C₂	semidirect
7. C₉×#396	C₂	semidirect
8. C₉×#394	C₂	semidirect
9. C₉×#394	C₂	semidirect
10. C₉×#392	C₂	semidirect
11. C₉×#390	C₂	semidirect
12. C₉×#388	C₂	semidirect
13. C₉×#386	C₂	semidirect
14. C₉×#386	C₂	semidirect
15. C₉×#385	C₂	semidirect
24. C₂²×D₄×C₉	C₂²	semidirect
27. C₂³×C₄×C₉	C₂²	semidirect
33. C₂×C₉×C₄⋊C₄	C₂²	semidirect
34. C₂×C₉×C₄⋊C₄	C₂²	semidirect
35. C₂×C₉×C₄⋊C₄	C₂²	semidirect
36. C₂×C₉×C₄⋊C₄	C₂²	semidirect
48. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
49. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
50. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
51. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
52. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
53. C₂×C₄²×C₉	C₂²	semidirect
54. C₉×#95	C₂²	semidirect
55. C₉×#95	C₂²	semidirect
56. C₉×#95	C₂²	semidirect
57. C₉×#95	C₂²	semidirect
105. C₂×D₄×C₉	D₄	semidirect
142. C₉×C₂²⋊C₄	D₄	semidirect
143. C₉×C₂²⋊C₄	D₄	semidirect
145. #2424	C₉	direct (N × H)
270. C₂×#121	C₂×C₉	semidirect
271. C₂×#121	C₂×C₉	semidirect
272. C₂×#120	C₂×C₉	semidirect
273. C₂×#120	C₂×C₉	semidirect
274. C₂×C₄×D₄	C₂×C₉	semidirect
275. C₂²×C₂²⋊C₄	C₂×C₉	semidirect
276. #396	C₂×C₉	semidirect
277. #394	C₂×C₉	semidirect
278. #394	C₂×C₉	semidirect
279. #392	C₂×C₉	semidirect
280. #390	C₂×C₉	semidirect
281. #388	C₂×C₉	semidirect
282. #386	C₂×C₉	semidirect
283. #386	C₂×C₉	semidirect
284. #385	C₂×C₉	semidirect
392. C₂²×C₉	#121	semidirect
417. C₂²×D₄	C₂²×C₉	semidirect
420. C₂³×C₄	C₂²×C₉	semidirect
426. C₂×C₄⋊C₄	C₂²×C₉	semidirect
427. C₂×C₄⋊C₄	C₂²×C₉	semidirect
428. C₂×C₄⋊C₄	C₂²×C₉	semidirect
429. C₂×C₄⋊C₄	C₂²×C₉	semidirect
441. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
442. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
443. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
444. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
445. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
446. C₂×C₄²	C₂²×C₉	semidirect
447. #95	C₂²×C₉	semidirect
448. #95	C₂²×C₉	semidirect
449. #95	C₂²×C₉	semidirect
450. #95	C₂²×C₉	semidirect
578. C₂×D₄	D₄×C₉	semidirect
615. C₂²⋊C₄	D₄×C₉	semidirect
616. C₂²⋊C₄	D₄×C₉	semidirect
671. C₉	#2424	direct (N × H)
802. C₂²	C₉×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#121	2
C₂×C₉×#120	2
C₂×C₄×D₄×C₉	2
C₂²×C₉×C₂²⋊C₄	2
C₉×#396	2
C₉×#394	2
C₉×#392	2
C₉×#390	2
C₉×#388	2
C₉×#386	2
C₉×#385	2
C₃×#2424	3

Subgroups — C9×#2424 #11767145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2424 #11767145