Subgroups — C₂×C₉×#930 #13153545

Order 1728.

1514 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×#67	C₂	1	2	yes	maximal, complemented
3	C₂²×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#930	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#930	C₃	1	1	yes	maximal, characteristic
8	C₂×C₉×#121	—	3	1	no	maximal
9	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
10	C₂³×D₃×C₉	C₂²	1	2	yes	—
11	C₂²×C₃×C₄×C₉	—	2	4	no	—
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₉	C₂²	1	4	yes	complemented
15	C₂×C₉×#67	—	2	8	no	—
16	C₂×C₉×#67	C₂²	1	8	yes	complemented
17	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
18	C₂×C₉×D₁₂	—	2	4	no	—
19	C₂×C₉×D₁₂	C₂²	1	4	yes	complemented
20	C₉×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
21	C₉×C₄⋊Dic₃	C₂²	1	4	yes	complemented
22	C₂³×C₃²×C₄	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₃×#67	C₂×C₃	1	2	yes	—
24	C₂²×C₃×D₁₂	C₂×C₃	1	1	yes	characteristic
25	C₃×#930	C₂×C₃	1	8	yes	—
26	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	—
27	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
28	C₂²×D₄×C₉	—	3	2	no	—
29	C₂²×D₄×C₉	—	3	1	no	—
30	C₂³×C₄×C₉	—	2	1	no	—
31	C₂³×C₄×C₉	D₃	1	1	yes	characteristic, complemented
32	C₉×#121	—	3	8	no	—
33	C₂×C₉×C₄⋊C₄	—	3	1	no	—
34	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
35	C₂³×C₃×C₉	—	2	2	no	—
36	C₂³×C₃×C₉	—	2	2	no	—
37	C₂³×C₃×C₉	D₄	1	4	yes	complemented
38	C₂³×C₃×C₉	C₂³	1	2	yes	—
39	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
40	C₂²×D₃×C₉	—	2	4	no	—
41	C₂²×D₃×C₉	—	2	4	no	—
42	C₂²×D₃×C₉	—	2	4	no	—
43	C₂²×D₃×C₉	C₂³	1	4	yes	—
44	C₂×C₃×C₄×C₉	—	2	2	no	—
45	C₂×C₃×C₄×C₉	—	2	8	no	—
46	C₂×C₃×C₄×C₉	D₄	1	4	yes	complemented
47	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
48	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
49	C₉×#67	—	2	16	no	—
50	C₂×C₉×Dic₃	—	2	4	no	—
51	C₂×C₉×Dic₃	C₂³	1	4	yes	—
52	C₉×D₁₂	—	2	8	no	—
53	C₂×C₃×#121	—	3	1	no	—
54	C₂×#930	C₉	1	1	yes	characteristic, direct product factor
55	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
56	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
57	C₂²×C₃²×C₄	—	2	4	no	—
58	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
59	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
60	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
61	C₂×C₃×#67	—	2	8	no	—
62	C₂×C₃×#67	C₂²×C₃	1	8	yes	—
63	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
64	C₂×C₃×D₁₂	—	2	4	no	—
65	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
66	C₂⁴×C₉	—	2	1	no	—
67	C₂⁴×C₉	—	3	2	no	—
68	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
69	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
70	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
71	C₂×D₄×C₉	—	3	8	no	—
72	C₂×D₄×C₉	—	3	4	no	—
73	C₂×D₄×C₉	—	6	8	no	—
74	C₂×D₄×C₉	—	6	4	no	—
75	C₂²×C₄×C₉	—	2	8	no	—
76	C₂²×C₄×C₉	—	2	1	no	—
77	C₂²×C₄×C₉	—	2	1	no	—
78	C₂²×C₄×C₉	—	2	4	no	—
79	C₂²×C₄×C₉	—	2	4	no	—
80	C₂²×C₄×C₉	—	3	2	no	—
81	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
83	C₂²×C₄×C₉	C₂×D₃	1	4	yes	complemented
84	C₉×C₄⋊C₄	—	3	4	no	—
85	C₉×C₂²⋊C₄	—	3	8	no	—
86	C₂²×C₃×C₉	—	2	8	no	—
87	C₂²×C₃×C₉	—	2	2	no	—
88	C₂²×C₃×C₉	—	2	2	no	—
89	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
90	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
91	C₂²×C₃×C₉	C₂×D₄	1	4	yes	complemented
92	C₂²×C₃×C₉	#41	1	2	yes	—
93	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
94	C₂×D₃×C₉	—	2	4	no	—
95	C₂×D₃×C₉	—	2	4	no	—
96	C₂×D₃×C₉	—	2	4	no	—
97	C₂×D₃×C₉	—	4	8	no	—
98	C₃×C₄×C₉	—	2	2	no	—
99	C₃×C₄×C₉	C₂×D₄	1	4	yes	complemented
100	C₉×Dic₃	—	2	4	no	—
101	C₂²×C₃×D₄	—	3	2	no	—
102	C₂²×C₃×D₄	—	3	1	no	—
103	C₂³×C₃×C₄	—	2	1	no	—
104	C₂³×C₃×C₄	C₂×C₉	1	1	yes	characteristic, complemented
105	C₂³×C₃×C₄	C₃×D₃	1	1	yes	characteristic
106	C₂²×#67	C₂×C₉	1	2	yes	complemented
107	C₂²×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
108	C₃×#121	—	3	8	no	—
109	C₂×C₃×C₄⋊C₄	—	3	1	no	—
110	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
111	#930	C₂×C₉	1	8	yes	direct product factor
112	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	2	yes	complemented
113	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
114	C₂³×C₃²	—	2	2	no	—
115	C₂³×C₃²	—	2	2	no	—
116	C₂³×C₃²	C₃×D₄	1	4	yes	—
117	C₂³×C₃²	C₂³×C₃	1	2	yes	—
118	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
119	C₂²×C₃×D₃	—	2	4	no	—
120	C₂²×C₃×D₃	—	2	4	no	—
121	C₂²×C₃×D₃	—	2	4	no	—
122	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
123	C₂×C₃²×C₄	—	2	2	no	—
124	C₂×C₃²×C₄	—	2	8	no	—
125	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
126	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
127	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
128	C₃×#67	—	2	16	no	—
129	C₂×C₃×Dic₃	—	2	4	no	—
130	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
131	C₃×D₁₂	—	2	8	no	—
132	C₂³×C₉	—	2	4	no	—
133	C₂³×C₉	—	2	4	no	—
134	C₂³×C₉	—	2	2	no	—
135	C₂³×C₉	—	2	2	no	—
136	C₂³×C₉	—	2	4	no	—
137	C₂³×C₉	—	2	2	no	—
138	C₂³×C₉	—	2	1	no	—
139	C₂³×C₉	—	3	4	no	—
140	C₂³×C₉	—	6	4	no	—
141	C₂³×C₉	—	6	4	no	—
142	C₂³×C₉	—	6	4	no	—
143	C₂³×C₉	D₁₂	1	4	yes	complemented
144	C₂³×C₉	C₂²×D₃	1	2	yes	—
145	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
146	D₄×C₉	—	6	16	no	—
147	D₄×C₉	—	6	8	no	—
148	C₂×C₄×C₉	—	2	4	no	—
149	C₂×C₄×C₉	—	2	16	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	2	8	no	—
152	C₂×C₄×C₉	—	2	4	no	—
153	C₂×C₄×C₉	—	2	2	no	—
154	C₂×C₄×C₉	—	2	2	no	—
155	C₂×C₄×C₉	—	3	4	no	—
156	C₂×C₄×C₉	—	6	4	no	—
157	C₂×C₄×C₉	#67	1	4	yes	complemented
158	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
159	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
160	C₂×#121	—	3	1	no	Sylow
161	C₂×C₃×C₉	—	2	4	no	—
162	C₂×C₃×C₉	#121	1	4	yes	complemented
163	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
166	D₃×C₉	—	4	4	no	—
167	C₂⁴×C₃	—	2	1	no	—
168	C₂⁴×C₃	—	3	2	no	—
169	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
170	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
171	C₂³×D₃	C₂²×C₉	1	2	yes	—
172	C₂×C₃×D₄	—	3	8	no	—
173	C₂×C₃×D₄	—	3	4	no	—
174	C₂×C₃×D₄	—	6	8	no	—
175	C₂×C₃×D₄	—	6	4	no	—
176	C₂²×C₃×C₄	—	2	8	no	—
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	—	2	1	no	—
181	C₂²×C₃×C₄	—	2	4	no	—
182	C₂²×C₃×C₄	—	3	2	no	—
183	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂²×C₉	1	4	yes	complemented
186	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
189	C₂×#67	—	2	8	no	—
190	C₂×#67	C₂²×C₉	1	8	yes	complemented
191	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
192	C₂×D₁₂	—	2	4	no	—
193	C₂×D₁₂	C₂²×C₉	1	4	yes	complemented
194	C₃×C₄⋊C₄	—	3	4	no	—
195	C₃×C₂²⋊C₄	—	3	8	no	—
196	(C₂×D₃)⋊C₄	C₂²×C₉	1	8	yes	complemented
197	C₄⋊Dic₃	C₂²×C₉	1	4	yes	complemented
198	C₂²×C₃²	—	2	8	no	—
199	C₂²×C₃²	—	2	2	no	—
200	C₂²×C₃²	—	2	2	no	—
201	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
202	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
203	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
204	C₂²×C₃²	C₃×#41	1	2	yes	—
205	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
206	C₂×C₃×D₃	—	2	4	no	—
207	C₂×C₃×D₃	—	2	4	no	—
208	C₂×C₃×D₃	—	2	4	no	—
209	C₂×C₃×D₃	—	4	8	no	—
210	C₃²×C₄	—	2	2	no	—
211	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
212	C₃×Dic₃	—	2	4	no	—
213	C₂²×C₉	—	2	4	no	—
214	C₂²×C₉	—	2	16	no	—
215	C₂²×C₉	—	2	4	no	—
216	C₂²×C₉	—	2	8	no	—
217	C₂²×C₉	—	2	2	no	—
218	C₂²×C₉	—	2	2	no	—
219	C₂²×C₉	—	2	1	no	—
220	C₂²×C₉	—	2	2	no	—
221	C₂²×C₉	—	2	4	no	—
222	C₂²×C₉	—	2	2	no	—
223	C₂²×C₉	—	2	2	no	—
224	C₂²×C₉	—	6	4	no	—
225	C₂²×C₉	—	6	4	no	—
226	C₂²×C₉	—	6	4	no	—
227	C₂²×C₉	—	12	8	no	—
228	C₂²×C₉	C₂×D₁₂	1	2	yes	—
229	C₂²×C₉	C₂×D₁₂	1	4	yes	complemented
230	C₂²×C₉	#235	1	2	yes	—
231	C₂²×C₉	C₂×#67	1	2	yes	—
232	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
233	C₄×C₉	—	2	4	no	—
234	C₄×C₉	—	2	2	no	—
235	C₄×C₉	—	2	4	no	—
236	C₄×C₉	—	6	4	no	—
237	C₄×C₉	C₂×#67	1	4	yes	complemented
238	C₂²×D₄	—	3	2	no	—
239	C₂²×D₄	—	3	1	no	—
240	C₂³×C₄	D₃×C₉	1	1	yes	characteristic, complemented
241	#121	—	3	8	no	—
242	C₂×C₄⋊C₄	—	3	1	no	—
243	C₂×C₂²⋊C₄	—	3	2	no	—
244	C₃×C₉	C₂×#121	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₃	—	2	4	no	—
246	C₂³×C₃	—	2	4	no	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	2	2	no	—
249	C₂³×C₃	—	2	2	no	—
250	C₂³×C₃	—	2	2	no	—
251	C₂³×C₃	—	2	4	no	—
252	C₂³×C₃	—	2	2	no	—
253	C₂³×C₃	—	2	1	no	—
254	C₂³×C₃	—	3	4	no	—
255	C₂³×C₃	—	6	4	no	—
256	C₂³×C₃	—	6	4	no	—
257	C₂³×C₃	—	6	4	no	—
258	C₂³×C₃	D₄×C₉	1	4	yes	complemented
259	C₂³×C₃	C₂³×C₉	1	2	yes	—
260	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
261	C₂³×C₃	C₃×D₁₂	1	4	yes	—
262	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
263	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
264	C₂²×D₃	—	2	4	no	—
265	C₂²×D₃	—	2	4	no	—
266	C₂²×D₃	—	2	4	no	—
267	C₂²×D₃	C₂³×C₉	1	4	yes	—
268	C₃×D₄	—	6	16	no	—
269	C₃×D₄	—	6	8	no	—
270	C₂×C₃×C₄	—	2	4	no	—
271	C₂×C₃×C₄	—	2	16	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	8	no	—
275	C₂×C₃×C₄	—	2	8	no	—
276	C₂×C₃×C₄	—	2	4	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	3	4	no	—
280	C₂×C₃×C₄	—	6	4	no	—
281	C₂×C₃×C₄	D₄×C₉	1	4	yes	complemented
282	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
283	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
284	C₂×C₃×C₄	C₃×#67	1	4	yes	—
285	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
286	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
287	#67	—	2	16	no	—
288	C₂×Dic₃	—	2	4	no	—
289	C₂×Dic₃	C₂³×C₉	1	4	yes	—
290	D₁₂	—	2	8	no	—
291	C₂×C₃²	—	2	4	no	—
292	C₂×C₃²	C₃×#121	1	4	yes	—
293	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
294	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
295	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
296	C₃×D₃	—	4	4	no	—
297	C₂×C₉	—	2	8	no	—
298	C₂×C₉	—	2	4	no	—
299	C₂×C₉	—	2	4	no	—
300	C₂×C₉	—	2	1	no	—
301	C₂×C₉	—	2	1	no	—
302	C₂×C₉	—	2	1	no	—
303	C₂×C₉	—	12	4	no	—
304	C₂×C₉	#930	1	4	yes	direct product factor
305	C₂×C₉	C₂²×D₁₂	1	1	yes	characteristic
306	C₂×C₉	C₂×#235	1	1	yes	characteristic
307	C₂×C₉	C₂²×#67	1	1	yes	characteristic
308	C₂⁴	—	3	2	no	—
309	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
310	C₂×D₄	—	3	8	no	—
311	C₂×D₄	—	3	4	no	—
312	C₂×D₄	—	6	8	no	—
313	C₂×D₄	—	6	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	3	2	no	—
316	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₃×C₉	1	4	yes	complemented
319	C₄⋊C₄	—	3	4	no	—
320	C₂²⋊C₄	—	3	8	no	—
321	C₂²×C₃	—	2	4	no	—
322	C₂²×C₃	—	2	4	no	—
323	C₂²×C₃	—	2	16	no	—
324	C₂²×C₃	—	2	8	no	—
325	C₂²×C₃	—	2	8	no	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	2	4	no	—
333	C₂²×C₃	—	2	2	no	—
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	6	4	no	—
336	C₂²×C₃	—	6	4	no	—
337	C₂²×C₃	—	6	4	no	—
338	C₂²×C₃	—	12	8	no	—
339	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
340	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
341	C₂²×C₃	C₂×D₄×C₉	1	4	yes	complemented
342	C₂²×C₃	C₉×#41	1	2	yes	—
343	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
344	C₂²×C₃	C₂×C₃×D₁₂	1	2	yes	—
345	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
346	C₂²×C₃	C₃×#235	1	2	yes	—
347	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
348	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
349	C₂×D₃	—	2	4	no	—
350	C₂×D₃	—	2	4	no	—
351	C₂×D₃	—	2	4	no	—
352	C₂×D₃	—	4	8	no	—
353	C₃×C₄	—	2	4	no	—
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	2	no	—
356	C₃×C₄	—	2	4	no	—
357	C₃×C₄	—	6	4	no	—
358	C₃×C₄	C₂×D₄×C₉	1	4	yes	complemented
359	C₃×C₄	C₂×C₃×#67	1	4	yes	—
360	Dic₃	—	2	4	no	—
361	C₃²	C₂×C₃×#121	1	1	yes	characteristic
362	C₉	—	2	1	no	—
363	C₉	C₂×#930	1	1	yes	characteristic, direct product factor
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	3	4	no	—
367	C₂³	—	6	4	no	—
368	C₂³	—	6	4	no	—
369	C₂³	—	6	4	no	—
370	C₂³	C₉×D₁₂	1	4	yes	complemented
371	C₂³	C₂²×D₃×C₉	1	2	yes	—
372	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
373	D₄	—	6	16	no	—
374	D₄	—	6	8	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	3	4	no	—
378	C₂×C₄	—	6	4	no	—
379	C₂×C₄	C₉×#67	1	4	yes	complemented
380	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
381	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
382	C₂×C₃	—	2	8	no	—
383	C₂×C₃	—	2	4	no	—
384	C₂×C₃	—	2	4	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	2	1	no	—
387	C₂×C₃	—	2	4	no	—
388	C₂×C₃	—	2	1	no	—
389	C₂×C₃	—	12	4	no	—
390	C₂×C₃	C₉×#121	1	4	yes	complemented
391	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
392	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
393	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
394	C₂×C₃	C₃×#930	1	4	yes	—
395	C₂×C₃	C₂²×C₃×D₁₂	1	1	yes	characteristic
396	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
397	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
398	D₃	—	4	4	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	8	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	6	4	no	—
403	C₂²	—	6	4	no	—
404	C₂²	—	6	4	no	—
405	C₂²	—	12	8	no	—
406	C₂²	C₂×C₉×D₁₂	1	2	yes	—
407	C₂²	C₂×C₉×D₁₂	1	4	yes	complemented
408	C₂²	C₉×#235	1	2	yes	—
409	C₂²	C₂×C₉×#67	1	2	yes	—
410	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	6	4	no	—
413	C₄	C₂×C₉×#67	1	4	yes	complemented
414	C₃	—	2	1	no	—
415	C₃	C₂×C₉×#121	1	1	yes	characteristic, complemented
416	C₃	C₂×C₃×#930	1	1	yes	characteristic
417	C₂	—	2	4	no	—
418	C₂	—	12	4	no	—
419	C₂	C₉×#930	1	4	yes	direct product factor
420	C₂	C₂²×C₉×D₁₂	1	1	yes	characteristic
421	C₂	C₂×C₉×#235	1	1	yes	characteristic
422	C₂	C₂²×C₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂³×C₃×C₄×C₉	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂×C₃×#930	C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂³×C₄×C₉	D₃
hypocenter	C₃	C₂×C₉×#121
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂³×C₄×C₉

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₄×C₉	C₂	semidirect
2. C₂²×C₉×#67	C₂	semidirect
3. C₂²×C₉×D₁₂	C₂	semidirect
4. C₉×#930	C₂	direct (N × H)
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
14. C₂²×C₃×C₄×C₉	C₂²	semidirect
16. C₂×C₉×#67	C₂²	semidirect
19. C₂×C₉×D₁₂	C₂²	semidirect
20. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
21. C₉×C₄⋊Dic₃	C₂²	semidirect
31. C₂³×C₄×C₉	D₃	semidirect
37. C₂³×C₃×C₉	D₄	semidirect
46. C₂×C₃×C₄×C₉	D₄	semidirect
54. C₂×#930	C₉	direct (N × H)
83. C₂²×C₄×C₉	C₂×D₃	semidirect
91. C₂²×C₃×C₉	C₂×D₄	semidirect
99. C₃×C₄×C₉	C₂×D₄	semidirect
104. C₂³×C₃×C₄	C₂×C₉	semidirect
106. C₂²×#67	C₂×C₉	semidirect
107. C₂²×D₁₂	C₂×C₉	semidirect
111. #930	C₂×C₉	direct (N × H)
112. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
113. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
143. C₂³×C₉	D₁₂	semidirect
157. C₂×C₄×C₉	#67	semidirect
162. C₂×C₃×C₉	#121	semidirect
185. C₂²×C₃×C₄	C₂²×C₉	semidirect
190. C₂×#67	C₂²×C₉	semidirect
193. C₂×D₁₂	C₂²×C₉	semidirect
196. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
197. C₄⋊Dic₃	C₂²×C₉	semidirect
229. C₂²×C₉	C₂×D₁₂	semidirect
237. C₄×C₉	C₂×#67	semidirect
240. C₂³×C₄	D₃×C₉	semidirect
244. C₃×C₉	C₂×#121	semidirect
258. C₂³×C₃	D₄×C₉	semidirect
281. C₂×C₃×C₄	D₄×C₉	semidirect
304. C₂×C₉	#930	direct (N × H)
318. C₂²×C₄	C₂×D₃×C₉	semidirect
341. C₂²×C₃	C₂×D₄×C₉	semidirect
358. C₃×C₄	C₂×D₄×C₉	semidirect
363. C₉	C₂×#930	direct (N × H)
370. C₂³	C₉×D₁₂	semidirect
379. C₂×C₄	C₉×#67	semidirect
390. C₂×C₃	C₉×#121	semidirect
407. C₂²	C₂×C₉×D₁₂	semidirect
413. C₄	C₂×C₉×#67	semidirect
415. C₃	C₂×C₉×#121	semidirect
419. C₂	C₉×#930	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄×C₉	2
C₂²×C₉×#67	2
C₂²×C₉×D₁₂	2
C₉×#930	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×C₄⋊Dic₃	2
C₂×C₃×#930	3
C₂×C₉×#121	3

Subgroups — C2×C9×#930 #13153545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#930 #13153545