Subgroups — C₉×#4730 #13141590

Order 1728.

422 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#815	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4730	C₃	1	1	yes	maximal, characteristic
9	C₉×#435	—	3	1	no	maximal
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₉×#67	C₄	1	1	yes	characteristic
12	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
15	C₉×#217	C₄	1	1	yes	characteristic
16	C₉×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
17	C₉×Dic₃⋊C₄	C₄	1	1	yes	characteristic
18	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₉×C₃⋊C₈	—	2	2	no	—
20	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₉×ΓL(1,𝔽₂₅)	—	2	2	no	—
23	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
24	C₂²×C₃×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
26	C₃²×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
27	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
28	C₃×#815	C₂×C₃	1	1	yes	characteristic
29	C₃×Dic₃⋊C₈	C₂×C₃	1	1	yes	characteristic
30	C₂×C₉×M₁₆	—	3	1	no	—
31	C₂²×C₈×C₉	—	3	1	no	—
32	C₄×D₄×C₉	—	3	1	no	—
33	C₉×C₄⋊C₈	—	3	1	no	—
34	C₉×C₂²⋊C₈	—	2	1	no	—
35	C₉×C₂²⋊C₈	—	3	1	no	—
36	C₉×C₂²⋊C₈	D₃	1	1	yes	characteristic, complemented
37	C₉×#97	—	3	1	no	—
38	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₉	—	2	1	no	—
41	C₂×C₃×C₄×C₉	—	2	1	no	—
42	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
44	C₉×#67	—	2	2	no	—
45	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
48	C₄×D₃×C₉	—	2	1	no	—
49	C₄×D₃×C₉	—	2	1	no	—
50	C₃×C₈×C₉	—	2	1	no	—
51	C₃×C₈×C₉	—	2	1	no	—
52	C₉×C₃⋊C₈	—	2	1	no	—
53	C₉×C₃⋊C₈	D₄	1	2	yes	complemented
54	C₃×#435	—	3	1	no	—
55	#4730	C₉	1	1	yes	characteristic, direct product factor
56	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₃×#67	C₃×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
61	C₃×#217	C₃×C₄	1	1	yes	characteristic
62	C₃×(C₂×D₃)⋊C₄	C₃×C₄	1	1	yes	characteristic
63	C₃×Dic₃⋊C₄	C₃×C₄	1	1	yes	characteristic
64	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃×C₃⋊C₈	—	2	2	no	—
66	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
68	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
69	C₂×D₄×C₉	—	3	1	no	—
70	C₂²×C₄×C₉	—	2	1	no	—
71	C₂²×C₄×C₉	—	3	1	no	—
72	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
73	C₉×M₁₆	—	6	2	no	—
74	C₂×C₈×C₉	—	2	1	no	—
75	C₂×C₈×C₉	—	2	1	no	—
76	C₂×C₈×C₉	—	3	1	no	—
77	C₂×C₈×C₉	—	3	1	no	—
78	C₂×C₈×C₉	—	6	2	no	—
79	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
80	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
81	C₉×C₄⋊C₄	—	3	1	no	—
82	C₉×C₂²⋊C₄	—	3	1	no	—
83	C₉×C₂²⋊C₄	—	3	1	no	—
84	C₄²×C₉	—	3	1	no	—
85	C₂²×C₃×C₉	—	2	1	no	—
86	C₂²×C₃×C₉	—	2	1	no	—
87	C₂²×C₃×C₉	M₁₆	1	2	yes	complemented
88	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
89	C₂×D₃×C₉	—	2	1	no	—
90	C₂×D₃×C₉	—	2	1	no	—
91	C₂×D₃×C₉	—	2	1	no	—
92	C₃×C₄×C₉	—	2	1	no	—
93	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
94	C₃×C₄×C₉	#41	1	1	yes	characteristic
95	C₉×Dic₃	—	2	1	no	—
96	C₉×Dic₃	—	2	1	no	—
97	C₉×Dic₃	—	2	1	no	—
98	C₂×C₃×M₁₆	—	3	1	no	—
99	C₂²×C₃×C₈	—	3	1	no	—
100	C₃×C₄×D₄	—	3	1	no	—
101	C₄×#67	C₂×C₉	1	1	yes	characteristic
102	C₂²×C₃⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
103	C₂×ΓL(1,𝔽₂₅)	C₂×C₉	1	1	yes	characteristic, complemented
104	C₃×C₄⋊C₈	—	3	1	no	—
105	C₃×C₂²⋊C₈	—	2	1	no	—
106	C₃×C₂²⋊C₈	—	3	1	no	—
107	C₃×C₂²⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
108	C₃×C₂²⋊C₈	C₃×D₃	1	1	yes	characteristic
109	C₃×#97	—	3	1	no	—
110	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
111	#815	C₂×C₉	1	1	yes	characteristic, complemented
112	Dic₃⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
113	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
114	C₂²×C₃×D₃	C₂×C₃×C₄	1	1	yes	characteristic
115	C₂×C₃²×C₄	—	2	1	no	—
116	C₂×C₃²×C₄	—	2	1	no	—
117	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
119	C₃×#67	—	2	2	no	—
120	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
121	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
123	C₃×C₄×D₃	—	2	1	no	—
124	C₃×C₄×D₃	—	2	1	no	—
125	C₂³×C₉	—	2	1	no	—
126	C₂³×C₉	—	3	1	no	—
127	C₂³×C₉	C₄×D₃	1	1	yes	characteristic
128	C₃²×C₈	—	2	1	no	—
129	C₃²×C₈	—	2	1	no	—
130	C₃×C₃⋊C₈	—	2	1	no	—
131	C₃×C₃⋊C₈	C₃×D₄	1	2	yes	—
132	D₄×C₉	—	6	2	no	—
133	C₂×C₄×C₉	—	2	1	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	—	3	1	no	—
138	C₂×C₄×C₉	—	3	1	no	—
139	C₂×C₄×C₉	—	3	1	no	—
140	C₂×C₄×C₉	—	4	1	no	—
141	C₂×C₄×C₉	—	4	1	no	—
142	C₂×C₄×C₉	—	6	1	no	—
143	C₂×C₄×C₉	—	6	1	no	—
144	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
145	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
146	C₈×C₉	—	2	1	no	—
147	C₈×C₉	—	2	1	no	—
148	C₈×C₉	—	3	2	no	—
149	C₈×C₉	—	4	1	no	—
150	C₈×C₉	—	4	1	no	—
151	C₈×C₉	—	6	1	no	—
152	#435	—	3	1	no	Sylow
153	C₂×C₃×C₉	—	2	2	no	—
154	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₃×C₉	C₂×M₁₆	1	1	yes	characteristic
156	C₂×C₃×C₉	#131	1	1	yes	characteristic
157	D₃×C₉	—	4	1	no	—
158	C₂×C₃×D₄	—	3	1	no	—
159	C₂²×C₃×C₄	—	2	1	no	—
160	C₂²×C₃×C₄	—	3	1	no	—
161	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
163	C₂×#67	C₄×C₉	1	1	yes	characteristic
164	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
165	C₃×M₁₆	—	6	2	no	—
166	C₂×C₃×C₈	—	2	1	no	—
167	C₂×C₃×C₈	—	2	1	no	—
168	C₂×C₃×C₈	—	3	1	no	—
169	C₂×C₃×C₈	—	3	1	no	—
170	C₂×C₃×C₈	—	6	2	no	—
171	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
172	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
173	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
174	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
175	C₃×C₄⋊C₄	—	3	1	no	—
176	C₃×C₂²⋊C₄	—	3	1	no	—
177	C₃×C₂²⋊C₄	—	3	1	no	—
178	C₃×C₄²	—	3	1	no	—
179	#217	C₄×C₉	1	1	yes	characteristic
180	(C₂×D₃)⋊C₄	C₄×C₉	1	1	yes	characteristic
181	Dic₃⋊C₄	C₄×C₉	1	1	yes	characteristic
182	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
183	C₂×C₃⋊C₈	—	2	2	no	—
184	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
185	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
186	ΓL(1,𝔽₂₅)	—	2	2	no	—
187	C₂²×C₃²	—	2	1	no	—
188	C₂²×C₃²	—	2	1	no	—
189	C₂²×C₃²	C₃×M₁₆	1	2	yes	—
190	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
191	C₂×C₃×D₃	—	2	1	no	—
192	C₂×C₃×D₃	—	2	1	no	—
193	C₂×C₃×D₃	—	2	1	no	—
194	C₃²×C₄	—	2	1	no	—
195	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
196	C₃²×C₄	C₃×#41	1	1	yes	characteristic
197	C₃×Dic₃	—	2	1	no	—
198	C₃×Dic₃	—	2	1	no	—
199	C₃×Dic₃	—	2	1	no	—
200	C₂²×C₉	—	2	1	no	—
201	C₂²×C₉	—	2	1	no	—
202	C₂²×C₉	—	2	2	no	—
203	C₂²×C₉	—	2	1	no	—
204	C₂²×C₉	—	4	1	no	—
205	C₂²×C₉	—	4	1	no	—
206	C₂²×C₉	—	6	1	no	—
207	C₂²×C₉	—	6	1	no	—
208	C₂²×C₉	—	6	1	no	—
209	C₂²×C₉	ΓL(1,𝔽₂₅)	1	2	yes	complemented
210	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
211	C₄×C₉	—	2	1	no	—
212	C₄×C₉	—	2	1	no	—
213	C₄×C₉	—	2	1	no	—
214	C₄×C₉	—	4	1	no	—
215	C₄×C₉	—	6	1	no	—
216	C₄×C₉	—	6	1	no	—
217	C₄×C₉	—	6	1	no	—
218	C₄×C₉	D₃×D₄	1	1	yes	characteristic
219	C₄×C₉	#237	1	1	yes	characteristic
220	C₂×M₁₆	—	3	1	no	—
221	C₂²×C₈	—	3	1	no	—
222	C₄×D₄	—	3	1	no	—
223	C₄⋊C₈	—	3	1	no	—
224	C₂²⋊C₈	—	3	1	no	—
225	C₂²⋊C₈	D₃×C₉	1	1	yes	characteristic, complemented
226	#97	—	3	1	no	—
227	C₃×C₉	#435	1	1	yes	characteristic, complemented, Sylow
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	3	1	no	—
230	C₂³×C₃	C₂×C₄×C₉	1	1	yes	characteristic
231	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
232	C₂²×D₃	C₂×C₄×C₉	1	1	yes	characteristic
233	C₃×D₄	—	6	2	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	3	1	no	—
241	C₂×C₃×C₄	—	3	1	no	—
242	C₂×C₃×C₄	—	3	1	no	—
243	C₂×C₃×C₄	—	4	1	no	—
244	C₂×C₃×C₄	—	4	1	no	—
245	C₂×C₃×C₄	—	6	1	no	—
246	C₂×C₃×C₄	—	6	1	no	—
247	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
249	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
251	#67	—	2	2	no	—
252	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
253	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
254	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
255	C₄×D₃	—	2	1	no	—
256	C₄×D₃	—	2	1	no	—
257	C₃×C₈	—	2	1	no	—
258	C₃×C₈	—	2	1	no	—
259	C₃×C₈	—	2	1	no	—
260	C₃×C₈	—	2	1	no	—
261	C₃×C₈	—	3	2	no	—
262	C₃×C₈	—	4	1	no	—
263	C₃×C₈	—	4	1	no	—
264	C₃×C₈	—	6	1	no	—
265	C₃⋊C₈	—	2	1	no	—
266	C₃⋊C₈	D₄×C₉	1	2	yes	complemented
267	C₂×C₃²	—	2	2	no	—
268	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
269	C₂×C₃²	C₂×C₃×M₁₆	1	1	yes	characteristic
270	C₂×C₃²	C₃×#131	1	1	yes	characteristic
271	C₃×D₃	—	4	1	no	—
272	C₂×C₉	—	2	2	no	—
273	C₂×C₉	—	2	1	no	—
274	C₂×C₉	—	2	1	no	—
275	C₂×C₉	—	2	1	no	—
276	C₂×C₉	—	4	2	no	—
277	C₂×C₉	—	12	1	no	—
278	C₂×C₉	#67⋊C₄	1	1	yes	characteristic
279	C₂×C₉	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
280	C₂×C₉	#907	1	1	yes	characteristic
281	C₂×D₄	—	3	1	no	—
282	C₂²×C₄	—	3	1	no	—
283	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
284	M₁₆	—	6	2	no	—
285	C₂×C₈	—	3	1	no	—
286	C₂×C₈	—	3	1	no	—
287	C₂×C₈	—	6	2	no	—
288	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
289	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
290	C₄⋊C₄	—	3	1	no	—
291	C₂²⋊C₄	—	3	1	no	—
292	C₂²⋊C₄	—	3	1	no	—
293	C₄²	—	3	1	no	—
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	4	1	no	—
302	C₂²×C₃	—	6	1	no	—
303	C₂²×C₃	—	6	1	no	—
304	C₂²×C₃	—	6	1	no	—
305	C₂²×C₃	C₉×M₁₆	1	2	yes	complemented
306	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
307	C₂²×C₃	C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
308	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
309	C₂×D₃	—	2	1	no	—
310	C₂×D₃	—	2	1	no	—
311	C₂×D₃	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	4	1	no	—
317	C₃×C₄	—	6	1	no	—
318	C₃×C₄	—	6	1	no	—
319	C₃×C₄	—	6	1	no	—
320	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
321	C₃×C₄	C₉×#41	1	1	yes	characteristic
322	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
323	C₃×C₄	C₃×#237	1	1	yes	characteristic
324	Dic₃	—	2	1	no	—
325	Dic₃	—	2	1	no	—
326	Dic₃	—	2	1	no	—
327	C₃²	C₃×#435	1	1	yes	characteristic
328	C₉	—	2	1	no	—
329	C₉	#4730	1	1	yes	characteristic, direct product factor
330	C₂³	—	3	1	no	—
331	C₂³	C₄×D₃×C₉	1	1	yes	characteristic
332	D₄	—	6	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	3	1	no	—
336	C₂×C₄	—	3	1	no	—
337	C₂×C₄	—	3	1	no	—
338	C₂×C₄	—	6	1	no	—
339	C₂×C₄	—	6	1	no	—
340	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	2	1	no	—
344	C₈	—	3	2	no	—
345	C₈	—	6	1	no	—
346	C₂×C₃	—	2	2	no	—
347	C₂×C₃	—	2	2	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	2	1	no	—
351	C₂×C₃	—	4	2	no	—
352	C₂×C₃	—	12	1	no	—
353	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
354	C₂×C₃	C₂×C₉×M₁₆	1	1	yes	characteristic
355	C₂×C₃	C₉×#131	1	1	yes	characteristic
356	C₂×C₃	C₃×#67⋊C₄	1	1	yes	characteristic
357	C₂×C₃	C₂×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
358	C₂×C₃	C₃×#907	1	1	yes	characteristic
359	D₃	—	4	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	6	1	no	—
363	C₂²	—	6	1	no	—
364	C₂²	—	6	1	no	—
365	C₂²	C₉×ΓL(1,𝔽₂₅)	1	2	yes	complemented
366	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	6	1	no	—
369	C₄	—	6	1	no	—
370	C₄	—	6	1	no	—
371	C₄	D₃×D₄×C₉	1	1	yes	characteristic
372	C₄	C₉×#237	1	1	yes	characteristic
373	C₃	—	2	1	no	—
374	C₃	C₉×#435	1	1	yes	characteristic, complemented
375	C₃	C₃×#4730	1	1	yes	characteristic
376	C₂	—	2	2	no	—
377	C₂	—	12	1	no	—
378	C₂	C₉×#67⋊C₄	1	1	yes	characteristic
379	C₂	C₂×C₉×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
380	C₂	C₉×#907	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×C₂²⋊C₈	C₂
socle	C₂²×C₃²	C₂²×C₃×C₄
prime radical	C₂×C₃×#67	C₃×C₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×C₂²⋊C₈	D₃
hypocenter	C₃	C₉×#435
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₉×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₉×C₃⋊C₈	C₂	semidirect
3. C₂×C₉×ΓL(1,𝔽₂₅)	C₂	semidirect
4. C₃×C₉×C₂²⋊C₈	C₂	semidirect
5. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
6. C₉×#815	C₂	semidirect
7. C₉×Dic₃⋊C₈	C₂	semidirect
36. C₉×C₂²⋊C₈	D₃	semidirect
53. C₉×C₃⋊C₈	D₄	semidirect
55. #4730	C₉	direct (N × H)
87. C₂²×C₃×C₉	M₁₆	semidirect
102. C₂²×C₃⋊C₈	C₂×C₉	semidirect
103. C₂×ΓL(1,𝔽₂₅)	C₂×C₉	semidirect
107. C₃×C₂²⋊C₈	C₂×C₉	semidirect
110. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
111. #815	C₂×C₉	semidirect
112. Dic₃⋊C₈	C₂×C₉	semidirect
209. C₂²×C₉	ΓL(1,𝔽₂₅)	semidirect
225. C₂²⋊C₈	D₃×C₉	semidirect
227. C₃×C₉	#435	semidirect
266. C₃⋊C₈	D₄×C₉	semidirect
305. C₂²×C₃	C₉×M₁₆	semidirect
329. C₉	#4730	direct (N × H)
365. C₂²	C₉×ΓL(1,𝔽₂₅)	semidirect
374. C₃	C₉×#435	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₉×#67	2
C₂²×C₉×C₃⋊C₈	2
C₂×C₉×ΓL(1,𝔽₂₅)	2
C₃×C₉×C₂²⋊C₈	2
C₉×(C₂×D₃)⋊C₈	2
C₉×#815	2
C₉×Dic₃⋊C₈	2
C₃×#4730	3
C₉×#435	3

Subgroups — C9×#4730 #13141590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4730 #13141590