Subgroups — C₃×#10589625 #13152484

Order 1728.

958 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3697	C₂	1	1	yes	maximal, characteristic
2	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63454	C₂	1	2	yes	maximal, complemented
5	C₃×C₄⋊C₄×D₉	C₂	1	2	yes	maximal, complemented
6	C₃×#611⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×D₃₆	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×Dic₁₈	C₂	1	2	yes	maximal, complemented
9	C₃×#5523	—	3	1	no	maximal
10	#10589625	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₃×#611	C₂²	1	2	yes	—
13	C₂²×C₃×Dic₉	C₂²	1	2	yes	—
14	C₃×#3697	C₄	1	8	yes	complemented
15	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×D₉	C₂²	1	4	yes	—
17	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
18	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₃×C₄²×C₉	C₂²	1	2	yes	—
23	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	—
24	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
25	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
26	C₃×Dic₉⋊C₄	C₂²	1	4	yes	—
27	C₃×C₄×Dic₉	C₂²	1	4	yes	—
28	C₂×C₃×#235	—	3	1	no	—
29	C₃²×#117	D₃	1	1	yes	characteristic
30	C₂×C₃×C₄⋊Dic₃	—	3	1	no	—
31	C₃×#892	—	3	2	no	—
32	C₃×D₃×C₄⋊C₄	—	3	2	no	—
33	C₃×#67⋊C₄	—	3	4	no	—
34	C₃×C₄×D₁₂	—	3	2	no	—
35	C₃×C₄×Dic₆	—	3	2	no	—
36	C₂×#3697	C₂×C₃	1	1	yes	characteristic
37	C₉×#117	—	2	1	no	—
38	C₉×#117	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×C₄⋊Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
40	#63454	C₂×C₃	1	2	yes	complemented
41	C₄⋊C₄×D₉	C₂×C₃	1	2	yes	complemented
42	#611⋊C₄	C₂×C₃	1	4	yes	complemented
43	C₄×D₃₆	C₂×C₃	1	2	yes	complemented
44	C₄×Dic₁₈	C₂×C₃	1	2	yes	complemented
45	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
46	C₂²×C₃×D₉	C₂³	1	2	yes	—
47	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
48	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
49	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₃×#611	C₂×C₄	1	8	yes	complemented
53	C₂×C₃×Dic₉	—	4	2	no	—
54	C₂×C₃×Dic₉	C₂³	1	4	yes	—
55	C₂×C₃×Dic₉	C₂³	1	2	yes	—
56	C₃×D₃₆	C₂×C₄	1	4	yes	complemented
57	C₃×C₄×D₉	—	4	4	no	—
58	C₃×C₄×D₉	C₂×C₄	1	8	yes	complemented
59	C₃×Dic₁₈	C₂×C₄	1	4	yes	complemented
60	C₃×#520	—	9	1	no	—
61	#5523	—	3	1	no	—
62	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
63	C₂×C₃×#67	—	3	2	no	—
64	C₂²×C₃×Dic₃	—	3	2	no	—
65	C₃×#235	—	3	8	no	—
66	C₂×C₃×D₁₂	—	3	1	no	—
67	C₂×C₃×C₄×D₃	—	3	2	no	—
68	C₂×C₃×C₄×D₃	—	3	4	no	—
69	C₂×C₃×Dic₆	—	3	1	no	—
70	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
71	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
72	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
73	C₃²×C₄²	C₂×D₃	1	2	yes	—
74	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
75	C₃×C₄⋊Dic₃	—	3	2	no	—
76	C₃×C₄⋊Dic₃	—	3	2	no	—
77	C₃×Dic₃⋊C₄	—	3	4	no	—
78	C₃×C₄×Dic₃	—	3	4	no	—
79	C₂²×C₄×C₉	—	2	1	no	—
80	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
81	C₂×#611	C₂²×C₃	1	2	yes	—
82	C₂²×Dic₉	C₂²×C₃	1	2	yes	—
83	#3697	C₃×C₄	1	8	yes	complemented
84	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
86	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
87	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
88	C₉×C₄⋊C₄	—	2	1	no	—
89	C₉×C₄⋊C₄	—	2	1	no	—
90	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₉×C₂²⋊C₄	—	2	2	no	—
93	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	C₄²×C₉	—	2	2	no	—
95	C₄²×C₉	C₂²×C₃	1	2	yes	—
96	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
97	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
98	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
99	Dic₉⋊C₄	C₂²×C₃	1	4	yes	—
100	C₄×Dic₉	C₂²×C₃	1	4	yes	—
101	C₂²×C₃×C₉	—	2	1	no	—
102	C₂²×C₃×C₉	—	2	1	no	—
103	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
105	C₂×C₃×D₉	—	2	2	no	—
106	C₂×C₃×D₉	—	2	2	no	—
107	C₂×C₃×D₉	C₂²×C₄	1	4	yes	—
108	C₃×C₄×C₉	—	2	2	no	—
109	C₃×C₄×C₉	—	2	2	no	—
110	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
111	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
112	C₃×Dic₉	—	2	4	no	—
113	C₃×Dic₉	C₂²×C₄	1	4	yes	—
114	C₂×C₃×#41	—	9	1	no	—
115	C₂×#235	—	3	1	no	—
116	C₃×C₄×Q₈	—	9	2	no	—
117	C₃×C₄×D₄	—	9	4	no	—
118	C₃×C₄×D₄	—	9	2	no	—
119	C₃×#117	—	2	1	no	—
120	C₃×#117	—	9	2	no	—
121	C₃×#117	D₉	1	1	yes	characteristic, complemented
122	C₃×#117	C₃×D₃	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₄	—	9	1	no	—
124	C₂×C₃×C₄⋊C₄	—	9	2	no	—
125	C₂×C₄⋊Dic₃	—	3	1	no	—
126	#892	—	3	2	no	—
127	D₃×C₄⋊C₄	—	3	2	no	—
128	#67⋊C₄	—	3	4	no	—
129	C₄×D₁₂	—	3	2	no	—
130	C₄×Dic₆	—	3	2	no	—
131	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
132	C₂²×C₃×D₃	—	3	2	no	—
133	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
134	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
135	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
136	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
137	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
138	C₃×#67	—	3	8	no	—
139	C₂×C₃×Dic₃	—	3	2	no	—
140	C₂×C₃×Dic₃	—	3	4	no	—
141	C₂×C₃×Dic₃	—	12	2	no	—
142	C₃×D₁₂	—	3	4	no	—
143	C₃×C₄×D₃	—	3	8	no	—
144	C₃×C₄×D₃	—	12	4	no	—
145	C₃×Dic₆	—	3	4	no	—
146	C₂³×C₉	—	2	1	no	—
147	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
148	C₂²×D₉	C₂³×C₃	1	2	yes	—
149	C₂×C₄×C₉	—	2	4	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	2	no	—
153	C₂×C₄×C₉	—	2	2	no	—
154	C₂×C₄×C₉	C₂×C₃×C₄	1	4	yes	complemented
155	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
156	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
157	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
158	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
159	#611	C₂×C₃×C₄	1	8	yes	complemented
160	C₂×Dic₉	—	4	2	no	—
161	C₂×Dic₉	C₂³×C₃	1	4	yes	—
162	C₂×Dic₉	C₂³×C₃	1	2	yes	—
163	D₃₆	C₂×C₃×C₄	1	4	yes	complemented
164	C₄×D₉	—	4	4	no	—
165	C₄×D₉	C₂×C₃×C₄	1	8	yes	complemented
166	Dic₁₈	C₂×C₃×C₄	1	4	yes	complemented
167	#520	—	9	1	no	Sylow
168	C₂×C₃×C₉	—	2	2	no	—
169	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
172	C₃×D₉	—	2	4	no	—
173	C₃×#41	—	9	8	no	—
174	C₂×C₃×Q₈	—	9	1	no	—
175	C₂×C₃×D₄	—	9	2	no	—
176	C₂×C₃×D₄	—	9	1	no	—
177	C₂²×C₃×C₄	—	2	1	no	—
178	C₂²×C₃×C₄	—	9	2	no	—
179	C₂²×C₃×C₄	—	9	2	no	—
180	C₂²×C₃×C₄	—	9	4	no	—
181	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
183	C₂×#67	—	3	2	no	—
184	C₂²×Dic₃	—	3	2	no	—
185	#235	—	3	8	no	—
186	C₂×D₁₂	—	3	1	no	—
187	C₂×C₄×D₃	—	3	2	no	—
188	C₂×C₄×D₃	—	3	4	no	—
189	C₂×Dic₆	—	3	1	no	—
190	C₃×C₄⋊C₄	—	2	1	no	—
191	C₃×C₄⋊C₄	—	2	1	no	—
192	C₃×C₄⋊C₄	—	9	4	no	—
193	C₃×C₄⋊C₄	—	9	2	no	—
194	C₃×C₄⋊C₄	—	9	2	no	—
195	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
196	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
197	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	—	2	2	no	—
200	C₃×C₂²⋊C₄	—	9	4	no	—
201	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	—
202	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
203	C₃×C₄²	—	2	2	no	—
204	C₃×C₄²	—	9	4	no	—
205	C₃×C₄²	C₂×D₉	1	2	yes	—
206	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
207	(C₂×D₃)⋊C₄	—	3	4	no	—
208	C₄⋊Dic₃	—	3	2	no	—
209	C₄⋊Dic₃	—	3	2	no	—
210	Dic₃⋊C₄	—	3	4	no	—
211	C₄×Dic₃	—	3	4	no	—
212	C₂²×C₃²	—	2	1	no	—
213	C₂²×C₃²	—	2	1	no	—
214	C₂²×C₃²	C₂×C₄×D₃	1	2	yes	—
215	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
216	C₂×C₃×D₃	—	3	4	no	—
217	C₂×C₃×D₃	—	6	2	no	—
218	C₂×C₃×D₃	—	6	2	no	—
219	C₃²×C₄	—	2	2	no	—
220	C₃²×C₄	—	2	2	no	—
221	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
222	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
223	C₃×Dic₃	—	3	4	no	—
224	C₃×Dic₃	—	6	4	no	—
225	C₂²×C₉	—	2	1	no	—
226	C₂²×C₉	—	2	1	no	—
227	C₂²×C₉	—	2	1	no	—
228	C₂²×C₉	—	2	2	no	—
229	C₂²×C₉	—	4	1	no	—
230	C₂²×C₉	—	4	1	no	—
231	C₂²×C₉	C₂²×C₃×C₄	1	2	yes	—
232	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
233	C₂×D₉	—	2	2	no	—
234	C₂×D₉	—	2	2	no	—
235	C₂×D₉	C₂²×C₃×C₄	1	4	yes	—
236	C₄×C₉	—	2	2	no	—
237	C₄×C₉	—	2	2	no	—
238	C₄×C₉	—	2	2	no	—
239	C₄×C₉	—	2	2	no	—
240	C₄×C₉	—	4	2	no	—
241	C₄×C₉	—	4	2	no	—
242	C₄×C₉	C₂²×C₃×C₄	1	2	yes	—
243	C₄×C₉	C₂²×C₃×C₄	1	2	yes	—
244	Dic₉	—	2	4	no	—
245	Dic₉	C₂²×C₃×C₄	1	4	yes	—
246	C₂×#41	—	9	1	no	—
247	C₄×Q₈	—	9	2	no	—
248	C₄×D₄	—	9	4	no	—
249	C₄×D₄	—	9	2	no	—
250	#117	—	9	2	no	—
251	#117	C₃×D₉	1	1	yes	characteristic, complemented
252	C₂×C₄⋊C₄	—	9	1	no	—
253	C₂×C₄⋊C₄	—	9	2	no	—
254	C₃×C₉	#520	1	1	yes	characteristic, complemented, Sylow
255	C₂³×C₃	—	2	1	no	—
256	C₂³×C₃	—	9	2	no	—
257	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
258	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
259	C₂²×D₃	—	3	2	no	—
260	C₃×Q₈	—	9	4	no	—
261	C₃×D₄	—	9	8	no	—
262	C₃×D₄	—	9	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	9	2	no	—
269	C₂×C₃×C₄	—	9	8	no	—
270	C₂×C₃×C₄	—	9	4	no	—
271	C₂×C₃×C₄	—	36	4	no	—
272	C₂×C₃×C₄	—	36	2	no	—
273	C₂×C₃×C₄	C₄×D₉	1	4	yes	complemented
274	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
275	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
276	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
278	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
279	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
280	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
281	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
283	#67	—	3	8	no	—
284	C₂×Dic₃	—	3	2	no	—
285	C₂×Dic₃	—	3	4	no	—
286	C₂×Dic₃	—	12	2	no	—
287	D₁₂	—	3	4	no	—
288	C₄×D₃	—	3	8	no	—
289	C₄×D₃	—	12	4	no	—
290	Dic₆	—	3	4	no	—
291	C₂×C₃²	—	2	2	no	—
292	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
293	C₂×C₃²	#1009	1	1	yes	characteristic
294	C₂×C₃²	#1010	1	1	yes	characteristic
295	C₃×D₃	—	6	4	no	—
296	C₂×C₉	—	2	2	no	—
297	C₂×C₉	—	2	1	no	—
298	C₂×C₉	—	2	1	no	—
299	C₂×C₉	—	2	1	no	—
300	C₂×C₉	—	4	2	no	—
301	C₂×C₉	C₂³×C₃×C₄	1	1	yes	characteristic
302	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
303	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
304	D₉	—	2	4	no	—
305	#41	—	9	8	no	—
306	C₂×Q₈	—	9	1	no	—
307	C₂×D₄	—	9	2	no	—
308	C₂×D₄	—	9	1	no	—
309	C₂²×C₄	—	9	2	no	—
310	C₂²×C₄	—	9	2	no	—
311	C₂²×C₄	—	9	4	no	—
312	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
313	C₄⋊C₄	—	9	2	no	—
314	C₄⋊C₄	—	9	4	no	—
315	C₄⋊C₄	—	9	2	no	—
316	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
317	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
318	C₂²⋊C₄	—	9	4	no	—
319	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	—
320	C₄²	—	9	4	no	—
321	C₄²	C₂×C₃×D₉	1	2	yes	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	2	1	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	2	1	no	—
326	C₂²×C₃	—	2	1	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	4	1	no	—
329	C₂²×C₃	—	4	1	no	—
330	C₂²×C₃	—	9	4	no	—
331	C₂²×C₃	—	18	2	no	—
332	C₂²×C₃	—	18	2	no	—
333	C₂²×C₃	C₂×C₄×D₉	1	2	yes	—
334	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
335	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
336	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
337	C₂×D₃	—	3	4	no	—
338	C₂×D₃	—	6	2	no	—
339	C₂×D₃	—	6	2	no	—
340	C₃×C₄	—	2	2	no	—
341	C₃×C₄	—	2	2	no	—
342	C₃×C₄	—	2	2	no	—
343	C₃×C₄	—	2	2	no	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	—	4	2	no	—
347	C₃×C₄	—	4	2	no	—
348	C₃×C₄	—	9	4	no	—
349	C₃×C₄	—	18	4	no	—
350	C₃×C₄	C₂×C₄×D₉	1	2	yes	—
351	C₃×C₄	C₂×C₄×D₉	1	2	yes	—
352	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
353	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
354	Dic₃	—	3	4	no	—
355	Dic₃	—	6	4	no	—
356	C₃²	#5523	1	1	yes	characteristic
357	C₉	—	2	1	no	—
358	C₉	C₃×#520	1	1	yes	characteristic, complemented
359	C₂³	—	9	2	no	—
360	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
361	Q₈	—	9	4	no	—
362	D₄	—	9	8	no	—
363	D₄	—	9	4	no	—
364	C₂×C₄	—	9	2	no	—
365	C₂×C₄	—	9	8	no	—
366	C₂×C₄	—	9	4	no	—
367	C₂×C₄	—	36	4	no	—
368	C₂×C₄	—	36	2	no	—
369	C₂×C₄	C₃×C₄×D₉	1	4	yes	complemented
370	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
371	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
372	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
374	C₂×C₃	—	2	2	no	—
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	—	2	1	no	—
377	C₂×C₃	—	2	1	no	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	4	2	no	—
380	C₂×C₃	—	18	4	no	—
381	C₂×C₃	C₂²×C₄×D₉	1	1	yes	characteristic
382	C₂×C₃	#63715	1	1	yes	characteristic
383	C₂×C₃	#63716	1	1	yes	characteristic
384	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
385	C₂×C₃	C₃×#1009	1	1	yes	characteristic
386	C₂×C₃	C₃×#1010	1	1	yes	characteristic
387	D₃	—	6	4	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	9	4	no	—
391	C₂²	—	18	2	no	—
392	C₂²	—	18	2	no	—
393	C₂²	C₂×C₃×C₄×D₉	1	2	yes	—
394	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	9	4	no	—
398	C₄	—	18	4	no	—
399	C₄	C₂×C₃×C₄×D₉	1	2	yes	—
400	C₄	C₂×C₃×C₄×D₉	1	2	yes	—
401	C₃	—	2	1	no	—
402	C₃	#10589625	1	1	yes	characteristic, direct product factor
403	C₃	C₃×#5523	1	1	yes	characteristic
404	C₂	—	2	2	no	—
405	C₂	—	18	4	no	—
406	C₂	C₂²×C₃×C₄×D₉	1	1	yes	characteristic
407	C₂	C₃×#63715	1	1	yes	characteristic
408	C₂	C₃×#63716	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator	C₂×C₉	C₂³×C₃×C₄
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#117	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂×C₃×#3697	C₂
cosocle	C₂²×C₉	C₂⁴×C₃
hypercenter	C₃×#117	D₉
hypocenter	C₉	C₃×#520
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
2. C₃×C₉×#117	C₂	semidirect
3. C₂×C₃×C₄⋊Dic₉	C₂	semidirect
4. C₃×#63454	C₂	semidirect
5. C₃×C₄⋊C₄×D₉	C₂	semidirect
6. C₃×#611⋊C₄	C₂	semidirect
7. C₃×C₄×D₃₆	C₂	semidirect
8. C₃×C₄×Dic₁₈	C₂	semidirect
10. #10589625	C₃	direct (N × H)
14. C₃×#3697	C₄	semidirect
38. C₉×#117	C₂×C₃	semidirect
39. C₂×C₄⋊Dic₉	C₂×C₃	semidirect
40. #63454	C₂×C₃	semidirect
41. C₄⋊C₄×D₉	C₂×C₃	semidirect
42. #611⋊C₄	C₂×C₃	semidirect
43. C₄×D₃₆	C₂×C₃	semidirect
44. C₄×Dic₁₈	C₂×C₃	semidirect
47. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
52. C₃×#611	C₂×C₄	semidirect
56. C₃×D₃₆	C₂×C₄	semidirect
58. C₃×C₄×D₉	C₂×C₄	semidirect
59. C₃×Dic₁₈	C₂×C₄	semidirect
83. #3697	C₃×C₄	semidirect
121. C₃×#117	D₉	semidirect
154. C₂×C₄×C₉	C₂×C₃×C₄	semidirect
159. #611	C₂×C₃×C₄	semidirect
163. D₃₆	C₂×C₃×C₄	semidirect
165. C₄×D₉	C₂×C₃×C₄	semidirect
166. Dic₁₈	C₂×C₃×C₄	semidirect
251. #117	C₃×D₉	semidirect
254. C₃×C₉	#520	semidirect
273. C₂×C₃×C₄	C₄×D₉	semidirect
358. C₉	C₃×#520	semidirect
369. C₂×C₄	C₃×C₄×D₉	semidirect
402. C₃	#10589625	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×#3697	2
C₃×C₉×#117	2
C₂×C₃×C₄⋊Dic₉	2
C₃×#63454	2
C₃×C₄⋊C₄×D₉	2
C₃×#611⋊C₄	2
C₃×C₄×D₃₆	2
C₃×C₄×Dic₁₈	2
C₃×#5523	3
#10589625	3

Subgroups — C3×#10589625 #13152484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589625 #13152484