Subgroups — C₉×#2420 #11767141

Order 1152.

894 conjugacy classes of subgroups.

The subgroup lattice has 477 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
2	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#397	C₂	1	2	yes	maximal, complemented
4	C₉×#394	C₂	1	2	yes	maximal, complemented
5	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#386	C₂	1	2	yes	maximal, complemented
8	C₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#381	C₂	1	2	yes	maximal, complemented
10	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2420	C₃	1	1	yes	maximal, characteristic
13	C₂²×D₄×C₉	C₂²	1	2	yes	—
14	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₉	C₂²	1	2	yes	—
17	C₉×#121	—	2	4	no	—
18	C₄×D₄×C₉	—	2	4	no	—
19	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
31	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
32	C₉×#95	C₂²	1	1	yes	characteristic
33	C₉×#95	C₂²	1	1	yes	characteristic
34	C₉×#95	C₂²	1	2	yes	—
35	C₉×#95	C₂²	1	2	yes	—
36	C₉×#95	C₂²	1	2	yes	—
37	C₉×#95	C₂²	1	2	yes	—
38	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
40	C₃×#397	C₂×C₃	1	2	yes	—
41	C₃×#394	C₂×C₃	1	2	yes	—
42	C₃×#390	C₂×C₃	1	1	yes	characteristic
43	C₃×#389	C₂×C₃	1	1	yes	characteristic
44	C₃×#386	C₂×C₃	1	2	yes	—
45	C₃×#382	C₂×C₃	1	1	yes	characteristic
46	C₃×#381	C₂×C₃	1	2	yes	—
47	C₃×#380	C₂×C₃	1	1	yes	characteristic
48	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
49	C₂⁴×C₉	C₂³	1	2	yes	—
50	C₂⁴×C₉	C₂³	1	1	yes	characteristic
51	C₂×D₄×C₉	—	2	4	no	—
52	C₂×D₄×C₉	—	2	4	no	—
53	C₂×D₄×C₉	—	2	2	no	—
54	C₂×D₄×C₉	—	2	2	no	—
55	C₂×D₄×C₉	—	4	2	no	—
56	C₂×D₄×C₉	D₄	1	4	yes	—
57	C₂²×C₄×C₉	—	2	4	no	—
58	C₂²×C₄×C₉	—	2	2	no	—
59	C₂²×C₄×C₉	—	2	4	no	—
60	C₂²×C₄×C₉	—	2	2	no	—
61	C₂²×C₄×C₉	—	2	2	no	—
62	C₂²×C₄×C₉	—	4	2	no	—
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₉	C₂³	1	2	yes	—
67	C₂²×C₄×C₉	C₂³	1	2	yes	—
68	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	C₂³	1	2	yes	—
70	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₉×C₄⋊C₄	—	2	2	no	—
73	C₉×C₄⋊C₄	—	2	2	no	—
74	C₉×C₄⋊C₄	—	2	2	no	—
75	C₉×C₄⋊C₄	—	4	2	no	—
76	C₉×C₂²⋊C₄	—	2	4	no	—
77	C₉×C₂²⋊C₄	—	2	4	no	—
78	C₉×C₂²⋊C₄	—	2	2	no	—
79	C₉×C₂²⋊C₄	—	2	2	no	—
80	C₉×C₂²⋊C₄	—	4	2	no	—
81	C₉×C₂²⋊C₄	—	4	2	no	—
82	C₉×C₂²⋊C₄	—	4	2	no	—
83	C₄²×C₉	—	2	2	no	—
84	C₄²×C₉	—	2	2	no	—
85	#2420	C₉	1	1	yes	characteristic, direct product factor, Sylow
86	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
87	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
88	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
90	C₃×#121	—	2	4	no	—
91	C₃×C₄×D₄	—	2	4	no	—
92	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
102	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
103	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
105	C₃×#95	C₂²×C₃	1	1	yes	characteristic
106	C₃×#95	C₂²×C₃	1	1	yes	characteristic
107	C₃×#95	C₂²×C₃	1	2	yes	—
108	C₃×#95	C₂²×C₃	1	2	yes	—
109	C₃×#95	C₂²×C₃	1	2	yes	—
110	C₃×#95	C₂²×C₃	1	2	yes	—
111	C₂³×C₉	—	2	1	no	—
112	C₂³×C₉	—	2	1	no	—
113	C₂³×C₉	—	2	1	no	—
114	C₂³×C₉	—	2	2	no	—
115	C₂³×C₉	—	2	1	no	—
116	C₂³×C₉	—	2	2	no	—
117	C₂³×C₉	—	2	2	no	—
118	C₂³×C₉	—	2	2	no	—
119	C₂³×C₉	—	2	1	no	—
120	C₂³×C₉	—	2	2	no	—
121	C₂³×C₉	—	2	2	no	—
122	C₂³×C₉	—	2	1	no	—
123	C₂³×C₉	C₂×D₄	1	4	yes	—
124	C₂³×C₉	#41	1	2	yes	—
125	C₂³×C₉	C₂⁴	1	1	yes	characteristic
126	D₄×C₉	—	2	8	no	—
127	D₄×C₉	—	4	8	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	2	1	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	2	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	2	no	—
148	C₂×C₄×C₉	—	2	2	no	—
149	C₂×C₄×C₉	—	2	1	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	4	8	no	—
152	C₂×C₄×C₉	—	4	4	no	—
153	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
154	C₂×C₄×C₉	#41	1	2	yes	—
155	C₂×C₄×C₉	#41	1	2	yes	—
156	C₂×C₄×C₉	#41	1	2	yes	—
157	C₂×#121	C₂×C₉	1	1	yes	characteristic
158	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
159	#397	C₂×C₉	1	2	yes	complemented
160	#394	C₂×C₉	1	2	yes	complemented
161	#390	C₂×C₉	1	1	yes	characteristic, complemented
162	#389	C₂×C₉	1	1	yes	characteristic, complemented
163	#386	C₂×C₉	1	2	yes	complemented
164	#382	C₂×C₉	1	1	yes	characteristic, complemented
165	#381	C₂×C₉	1	2	yes	complemented
166	#380	C₂×C₉	1	1	yes	characteristic, complemented
167	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
168	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
169	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₃×D₄	—	2	4	no	—
171	C₂×C₃×D₄	—	2	4	no	—
172	C₂×C₃×D₄	—	2	2	no	—
173	C₂×C₃×D₄	—	2	2	no	—
174	C₂×C₃×D₄	—	4	2	no	—
175	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
176	C₂²×C₃×C₄	—	2	4	no	—
177	C₂²×C₃×C₄	—	2	2	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	—	2	2	no	—
180	C₂²×C₃×C₄	—	2	2	no	—
181	C₂²×C₃×C₄	—	4	2	no	—
182	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
186	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
187	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
188	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
191	C₃×C₄⋊C₄	—	2	2	no	—
192	C₃×C₄⋊C₄	—	2	2	no	—
193	C₃×C₄⋊C₄	—	2	2	no	—
194	C₃×C₄⋊C₄	—	4	2	no	—
195	C₃×C₂²⋊C₄	—	2	4	no	—
196	C₃×C₂²⋊C₄	—	2	4	no	—
197	C₃×C₂²⋊C₄	—	2	2	no	—
198	C₃×C₂²⋊C₄	—	2	2	no	—
199	C₃×C₂²⋊C₄	—	4	2	no	—
200	C₃×C₂²⋊C₄	—	4	2	no	—
201	C₃×C₂²⋊C₄	—	4	2	no	—
202	C₃×C₄²	—	2	2	no	—
203	C₃×C₄²	—	2	2	no	—
204	C₂²×C₉	—	2	4	no	—
205	C₂²×C₉	—	2	2	no	—
206	C₂²×C₉	—	2	4	no	—
207	C₂²×C₉	—	2	2	no	—
208	C₂²×C₉	—	2	4	no	—
209	C₂²×C₉	—	2	2	no	—
210	C₂²×C₉	—	4	1	no	—
211	C₂²×C₉	—	4	2	no	—
212	C₂²×C₉	—	4	1	no	—
213	C₂²×C₉	—	4	2	no	—
214	C₂²×C₉	—	4	1	no	—
215	C₂²×C₉	—	4	2	no	—
216	C₂²×C₉	—	4	1	no	—
217	C₂²×C₉	—	4	2	no	—
218	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
219	C₂²×C₉	C₂×#41	1	1	yes	characteristic
220	C₂²×C₉	C₂×#41	1	1	yes	characteristic
221	C₂²×C₉	C₂×#41	1	1	yes	characteristic
222	C₂²×C₉	C₂×#41	1	1	yes	characteristic
223	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
224	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
225	C₄×C₉	—	2	2	no	—
226	C₄×C₉	—	4	1	no	—
227	C₄×C₉	—	4	2	no	—
228	C₄×C₉	—	4	1	no	—
229	C₄×C₉	—	4	2	no	—
230	C₄×C₉	—	4	2	no	—
231	C₄×C₉	—	4	1	no	—
232	C₄×C₉	—	4	1	no	—
233	C₄×C₉	#123	1	4	yes	—
234	C₂²×D₄	C₂²×C₉	1	2	yes	—
235	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
236	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
237	C₂³×C₄	C₂²×C₉	1	2	yes	—
238	#121	—	2	4	no	—
239	C₄×D₄	—	2	4	no	—
240	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
245	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
246	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
249	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
250	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
251	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
253	#95	C₂²×C₉	1	1	yes	characteristic
254	#95	C₂²×C₉	1	1	yes	characteristic
255	#95	C₂²×C₉	1	2	yes	—
256	#95	C₂²×C₉	1	2	yes	—
257	#95	C₂²×C₉	1	2	yes	—
258	#95	C₂²×C₉	1	2	yes	—
259	C₂³×C₃	—	2	1	no	—
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	2	2	no	—
263	C₂³×C₃	—	2	1	no	—
264	C₂³×C₃	—	2	2	no	—
265	C₂³×C₃	—	2	2	no	—
266	C₂³×C₃	—	2	2	no	—
267	C₂³×C₃	—	2	1	no	—
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	—	2	2	no	—
270	C₂³×C₃	—	2	1	no	—
271	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
272	C₂³×C₃	C₃×#41	1	2	yes	—
273	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
274	C₃×D₄	—	2	8	no	—
275	C₃×D₄	—	4	8	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	4	8	no	—
300	C₂×C₃×C₄	—	4	4	no	—
301	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
302	C₂×C₃×C₄	C₃×#41	1	2	yes	—
303	C₂×C₃×C₄	C₃×#41	1	2	yes	—
304	C₂×C₃×C₄	C₃×#41	1	2	yes	—
305	C₂×C₉	—	4	4	no	—
306	C₂×C₉	—	4	2	no	—
307	C₂×C₉	C₂×#123	1	1	yes	characteristic
308	C₂×C₉	#529	1	1	yes	characteristic
309	C₂×C₉	#540	1	1	yes	characteristic
310	C₂×C₉	#546	1	1	yes	characteristic
311	C₂×C₉	#546	1	1	yes	characteristic
312	C₂×C₉	#553	1	1	yes	characteristic
313	C₂×C₉	#555	1	1	yes	characteristic
314	C₂⁴	C₂³×C₉	1	2	yes	—
315	C₂⁴	C₂³×C₉	1	1	yes	characteristic
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	D₄×C₉	1	4	yes	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
330	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
331	C₂²×C₄	C₂³×C₉	1	2	yes	—
332	C₂²×C₄	C₂³×C₉	1	2	yes	—
333	C₂²×C₄	C₂³×C₉	1	2	yes	—
334	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
335	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
336	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₂²×C₃	—	2	4	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	2	4	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	—	4	1	no	—
357	C₂²×C₃	—	4	2	no	—
358	C₂²×C₃	—	4	1	no	—
359	C₂²×C₃	—	4	2	no	—
360	C₂²×C₃	—	4	1	no	—
361	C₂²×C₃	—	4	2	no	—
362	C₂²×C₃	—	4	1	no	—
363	C₂²×C₃	—	4	2	no	—
364	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
365	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
366	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
367	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
368	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
369	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
371	C₃×C₄	—	2	2	no	—
372	C₃×C₄	—	4	1	no	—
373	C₃×C₄	—	4	2	no	—
374	C₃×C₄	—	4	2	no	—
375	C₃×C₄	—	4	2	no	—
376	C₃×C₄	—	4	1	no	—
377	C₃×C₄	—	4	1	no	—
378	C₃×C₄	—	4	1	no	—
379	C₃×C₄	C₃×#123	1	4	yes	—
380	C₉	#2420	1	1	yes	characteristic, direct product factor, Sylow
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	1	no	—
393	C₂³	C₂×D₄×C₉	1	4	yes	—
394	C₂³	C₉×#41	1	2	yes	—
395	C₂³	C₂⁴×C₉	1	1	yes	characteristic
396	D₄	—	2	8	no	—
397	D₄	—	4	8	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
424	C₂×C₄	C₉×#41	1	2	yes	—
425	C₂×C₄	C₉×#41	1	2	yes	—
426	C₂×C₄	C₉×#41	1	2	yes	—
427	C₂×C₃	—	4	4	no	—
428	C₂×C₃	—	4	2	no	—
429	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
430	C₂×C₃	C₃×#529	1	1	yes	characteristic
431	C₂×C₃	C₃×#540	1	1	yes	characteristic
432	C₂×C₃	C₃×#546	1	1	yes	characteristic
433	C₂×C₃	C₃×#546	1	1	yes	characteristic
434	C₂×C₃	C₃×#553	1	1	yes	characteristic
435	C₂×C₃	C₃×#555	1	1	yes	characteristic
436	C₂²	—	2	4	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	2	no	—
450	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
451	C₂²	C₂×C₉×#41	1	1	yes	characteristic
452	C₂²	C₂×C₉×#41	1	1	yes	characteristic
453	C₂²	C₂×C₉×#41	1	1	yes	characteristic
454	C₂²	C₂×C₉×#41	1	1	yes	characteristic
455	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	1	no	—
465	C₄	C₉×#123	1	4	yes	—
466	C₃	C₃×#2420	1	1	yes	characteristic
467	C₂	—	4	4	no	—
468	C₂	—	4	2	no	—
469	C₂	C₂×C₉×#123	1	1	yes	characteristic
470	C₂	C₉×#529	1	1	yes	characteristic
471	C₂	C₉×#540	1	1	yes	characteristic
472	C₂	C₉×#546	1	1	yes	characteristic
473	C₂	C₉×#546	1	1	yes	characteristic
474	C₂	C₉×#553	1	1	yes	characteristic
475	C₂	C₉×#555	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂×C₃×#121	C₂×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
2. C₂×C₄×D₄×C₉	C₂	semidirect
3. C₉×#397	C₂	semidirect
4. C₉×#394	C₂	semidirect
5. C₉×#390	C₂	semidirect
6. C₉×#389	C₂	semidirect
7. C₉×#386	C₂	semidirect
8. C₉×#382	C₂	semidirect
9. C₉×#381	C₂	semidirect
10. C₉×#380	C₂	semidirect
11. C₄×C₉×C₂²⋊C₄	C₂	semidirect
85. #2420	C₉	direct (N × H)
158. C₂×C₄×D₄	C₂×C₉	semidirect
159. #397	C₂×C₉	semidirect
160. #394	C₂×C₉	semidirect
161. #390	C₂×C₉	semidirect
162. #389	C₂×C₉	semidirect
163. #386	C₂×C₉	semidirect
164. #382	C₂×C₉	semidirect
165. #381	C₂×C₉	semidirect
166. #380	C₂×C₉	semidirect
167. C₄×C₂²⋊C₄	C₂×C₉	semidirect
380. C₉	#2420	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×C₉×#121	2
C₂×C₄×D₄×C₉	2
C₉×#397	2
C₉×#394	2
C₉×#390	2
C₉×#389	2
C₉×#386	2
C₉×#382	2
C₉×#381	2
C₉×#380	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2420	3

Subgroups — C9×#2420 #11767141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2420 #11767141